chapter 3 resource masters - math...
TRANSCRIPT
Chapter 3Resource Masters
Consumable WorkbooksMany of the worksheets contained in the Chapter Resource Masters bookletsare available as consumable workbooks in both English and Spanish.
Study Guide and Intervention Workbook 0-07-827753-1Study Guide and Intervention Workbook (Spanish) 0-07-827754-XSkills Practice Workbook 0-07-827747-7Skills Practice Workbook (Spanish) 0-07-827749-3Practice Workbook 0-07-827748-5Practice Workbook (Spanish) 0-07-827750-7
ANSWERS FOR WORKBOOKS The answers for Chapter 3 of these workbookscan be found in the back of this Chapter Resource Masters booklet.
Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Printed in the United States of America. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teachers, and families without charge; and be used solely in conjunction with Glencoe’s Algebra 1. Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher.
Send all inquiries to:The McGraw-Hill Companies8787 Orion PlaceColumbus, OH 43240-4027
ISBN: 0-07-827727-2 Algebra 1Chapter 3 Resource Masters
2 3 4 5 6 7 8 9 10 024 11 10 09 08 07 06 05 04 03
Glencoe/McGraw-Hill
© Glencoe/McGraw-Hill iii Glencoe Algebra 1
Contents
Vocabulary Builder . . . . . . . . . . . . . . . . vii
Lesson 3-1Study Guide and Intervention . . . . . . . . 137–138Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 139Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 140Reading to Learn Mathematics . . . . . . . . . . 141Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 142
Lesson 3-2Study Guide and Intervention . . . . . . . . 143–144Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 145Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 146Reading to Learn Mathematics . . . . . . . . . . 147Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 148
Lesson 3-3Study Guide and Intervention . . . . . . . . 149–150Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 151Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 152Reading to Learn Mathematics . . . . . . . . . . 153Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 154
Lesson 3-4Study Guide and Intervention . . . . . . . . 155–156Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 157Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 158Reading to Learn Mathematics . . . . . . . . . . 159Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 160
Lesson 3-5Study Guide and Intervention . . . . . . . . 161–162Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 163Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 164Reading to Learn Mathematics . . . . . . . . . . 165Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 166
Lesson 3-6Study Guide and Intervention . . . . . . . . 167–168Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 169Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 170Reading to Learn Mathematics . . . . . . . . . . 171Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 172
Lesson 3-7Study Guide and Intervention . . . . . . . . 173–174Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 175Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 176Reading to Learn Mathematics . . . . . . . . . . 177Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 178
Lesson 3-8Study Guide and Intervention . . . . . . . . 179–180Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 181Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 182Reading to Learn Mathematics . . . . . . . . . . 183Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 184
Lesson 3-9Study Guide and Intervention . . . . . . . . 185–186Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 187Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 188Reading to Learn Mathematics . . . . . . . . . . 189Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 190
Chapter 3 AssessmentChapter 3 Test, Form 1 . . . . . . . . . . . . 191–192Chapter 3 Test, Form 2A . . . . . . . . . . . 193–194Chapter 3 Test, Form 2B . . . . . . . . . . . 195–196Chapter 3 Test, Form 2C . . . . . . . . . . . 197–198Chapter 3 Test, Form 2D . . . . . . . . . . . 199–200Chapter 3 Test, Form 3 . . . . . . . . . . . . 201–202Chapter 3 Open-Ended Assessment . . . . . . 203Chapter 3 Vocabulary Test/Review . . . . . . . 204Chapter 3 Quizzes 1 & 2 . . . . . . . . . . . . . . . 205Chapter 3 Quizzes 3 & 4 . . . . . . . . . . . . . . . 206Chapter 3 Mid-Chapter Test . . . . . . . . . . . . 207Chapter 3 Cumulative Review . . . . . . . . . . . 208Chapter 3 Standardized Test Practice . . 209–210Unit 1 Test/Review (Ch. 1–3) . . . . . . . . 211–212
Standardized Test Practice Student Recording Sheet . . . . . . . . . . . . . . A1
ANSWERS . . . . . . . . . . . . . . . . . . . . . . A2–A39
© Glencoe/McGraw-Hill iv Glencoe Algebra 1
Teacher’s Guide to Using theChapter 3 Resource Masters
The Fast File Chapter Resource system allows you to conveniently file the resourcesyou use most often. The Chapter 3 Resource Masters includes the core materials neededfor Chapter 3. These materials include worksheets, extensions, and assessment options.The answers for these pages appear at the back of this booklet.
All of the materials found in this booklet are included for viewing and printing in theAlgebra 1 TeacherWorks CD-ROM.
Vocabulary Builder Pages vii–viiiinclude a student study tool that presentsup to twenty of the key vocabulary termsfrom the chapter. Students are to recorddefinitions and/or examples for each term.You may suggest that students highlight orstar the terms with which they are notfamiliar.
WHEN TO USE Give these pages tostudents before beginning Lesson 3-1.Encourage them to add these pages to theirAlgebra Study Notebook. Remind them toadd definitions and examples as theycomplete each lesson.
Study Guide and InterventionEach lesson in Algebra 1 addresses twoobjectives. There is one Study Guide andIntervention master for each objective.
WHEN TO USE Use these masters asreteaching activities for students who needadditional reinforcement. These pages canalso be used in conjunction with the StudentEdition as an instructional tool for studentswho have been absent.
Skills Practice There is one master foreach lesson. These provide computationalpractice at a basic level.
WHEN TO USE These masters can be used with students who have weakermathematics backgrounds or needadditional reinforcement.
Practice There is one master for eachlesson. These problems more closely followthe structure of the Practice and Applysection of the Student Edition exercises.These exercises are of average difficulty.
WHEN TO USE These provide additionalpractice options or may be used ashomework for second day teaching of thelesson.
Reading to Learn MathematicsOne master is included for each lesson. Thefirst section of each master asks questionsabout the opening paragraph of the lessonin the Student Edition. Additionalquestions ask students to interpret thecontext of and relationships among termsin the lesson. Finally, students are asked tosummarize what they have learned usingvarious representation techniques.
WHEN TO USE This master can be usedas a study tool when presenting the lessonor as an informal reading assessment afterpresenting the lesson. It is also a helpfultool for ELL (English Language Learner)students.
Enrichment There is one extensionmaster for each lesson. These activities mayextend the concepts in the lesson, offer anhistorical or multicultural look at theconcepts, or widen students’ perspectives onthe mathematics they are learning. Theseare not written exclusively for honorsstudents, but are accessible for use with alllevels of students.
WHEN TO USE These may be used asextra credit, short-term projects, or asactivities for days when class periods areshortened.
© Glencoe/McGraw-Hill v Glencoe Algebra 1
Assessment OptionsThe assessment masters in the Chapter 3Resources Masters offer a wide range ofassessment tools for intermediate and finalassessment. The following lists describe eachassessment master and its intended use.
Chapter Assessment CHAPTER TESTS• Form 1 contains multiple-choice questions
and is intended for use with basic levelstudents.
• Forms 2A and 2B contain multiple-choicequestions aimed at the average levelstudent. These tests are similar in formatto offer comparable testing situations.
• Forms 2C and 2D are composed of free-response questions aimed at the averagelevel student. These tests are similar informat to offer comparable testingsituations. Grids with axes are providedfor questions assessing graphing skills.
• Form 3 is an advanced level test withfree-response questions. Grids withoutaxes are provided for questions assessinggraphing skills.
All of the above tests include a free-response Bonus question.
• The Open-Ended Assessment includesperformance assessment tasks that aresuitable for all students. A scoring rubricis included for evaluation guidelines.Sample answers are provided forassessment.
• A Vocabulary Test, suitable for allstudents, includes a list of the vocabularywords in the chapter and ten questionsassessing students’ knowledge of thoseterms. This can also be used in conjunc-tion with one of the chapter tests or as areview worksheet.
Intermediate Assessment• Four free-response quizzes are included
to offer assessment at appropriateintervals in the chapter.
• A Mid-Chapter Test provides an optionto assess the first half of the chapter. It iscomposed of both multiple-choice andfree-response questions.
Continuing Assessment• The Cumulative Review provides
students an opportunity to reinforce andretain skills as they proceed throughtheir study of Algebra 1. It can also beused as a test. This master includes free-response questions.
• The Standardized Test Practice offerscontinuing review of algebra concepts invarious formats, which may appear onthe standardized tests that they mayencounter. This practice includes multiple-choice, grid-in, and quantitative-comparison questions. Bubble-in andgrid-in answer sections are provided onthe master.
Answers• Page A1 is an answer sheet for the
Standardized Test Practice questionsthat appear in the Student Edition onpages 186–187. This improves students’familiarity with the answer formats theymay encounter in test taking.
• The answers for the lesson-by-lessonmasters are provided as reduced pageswith answers appearing in red.
• Full-size answer keys are provided forthe assessment masters in this booklet.
Reading to Learn MathematicsVocabulary Builder
NAME ______________________________________________ DATE ____________ PERIOD _____
33
© Glencoe/McGraw-Hill vii Glencoe Algebra 1
Voca
bula
ry B
uild
erThis is an alphabetical list of the key vocabulary terms you will learn in Chapter 3.As you study the chapter, complete each term’s definition or description.Remember to add the page number where you found the term. Add these pages toyour Algebra Study Notebook to review vocabulary at the end of the chapter.
Vocabulary Term Found on Page Definition/Description/Example
consecutive integers
kuhn-SEH-kyuh-tihv
defining a variable
dimensional analysis
duh·MEHNCH·nuhl
equivalent equation
ih·KWIHV·luhnt
extremes
formula
identity
means
multi-step equations
(continued on the next page)
⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩
⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩
⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩
© Glencoe/McGraw-Hill viii Glencoe Algebra 1
Vocabulary Term Found on Page Definition/Description/Example
number theory
percent of change
percent of decrease
percent of increase
proportion
pruh·POHR·shun
ratio
rate
scale
solve an equation
weighted average
work backward
⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩
Reading to Learn MathematicsVocabulary Builder (continued)
NAME ______________________________________________ DATE ____________ PERIOD _____
33
Study Guide and InterventionWriting Equations
NAME ______________________________________________ DATE ____________ PERIOD _____
3-13-1
© Glencoe/McGraw-Hill 137 Glencoe Algebra 1
Less
on
3-1
Write Equations Writing equations is one strategy for solving problems. You can use avariable to represent an unspecified number or measure referred to in a problem. Then youcan write a verbal expression as an algebraic expression.
Translate eachsentence into an equation or aformula.
a. Ten times a number x is equal to2.8 times the difference y minus z.10 ! x " 2.8 ! ( y # z)The equation is 10x " 2.8( y # z).
b. A number m minus 8 is the sameas a number n divided by 2.m # 8 " n $ 2The equation is m # 8 " .
c. The area of a rectangle equals thelength times the width. Translatethis sentence into a formula.Let A " area, ! " length, and w " width.Formula: Area equals length timeswidth.A " ! ! wThe formula for the area of arectangle is A " !w.
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Use the Four-Step Problem-Solving Plan.The population of the United States in 2001was about 284,000,000, and the land area ofthe United States is about 3,500,000 squaremiles. Find the average number of peopleper square mile in the United States.Source: www.census.gov
Step 1 Explore You know that there are284,000,000 people. You want to knowthe number of people per square mile.
Step 2 Plan Write an equation to represent thesituation. Let p represent the number ofpeople per square mile.3,500,000 ! p " 284,000,000
Step 3 Solve 3,500,000 ! p " 284,000,000.3,500,000p " 284,000,000 Divide each side by
p ! 81.14 3,500,000.
There about 81 people per square mile.Step 4 Examine If there are 81 people per
square mile and there are 3,500,000square miles, 81 ! 3,500,000 "283,500,000, or about 284,000,000 people.The answer makes sense.
Example 1Example 1 Example 2Example 2
ExercisesExercises
Translate each sentence into an equation or formula.
1. Three times a number t minus twelve equals forty.
2. One-half of the difference of a and b is 54.
3. Three times the sum of d and 4 is 32.
4. The area A of a circle is the product of & and the radius r squared.
WEIGHT LOSS For Exercises 5–6, use the following information.
Lou wants to lose weight to audition for a part in a play. He weighs 160 pounds now. Hewants to weigh 150 pounds.
5. If p represents the number of pounds he wants to lose, write an equation to representthis situation.
6. How many pounds does he need to lose to reach his goal?
© Glencoe/McGraw-Hill 138 Glencoe Algebra 1
Write Verbal Sentences You can translate equations into verbal sentences.
Translate each equation into a verbal sentence.
a. 4n ! 8 " 12.
4n # 8 " 12Four times n minus eight equals twelve.
b. a2 # b2 " c2
a2 ' b2 " c2
The sum of the squares of a and b is equal to the square of c.
Translate each equation into a verbal sentence.
1. 4a # 5 " 23 2. 10 ' k " 4k
3. 6xy " 24 4. x2 ' y2 " 8
5. p ' 3 " 2p 6. b " (h # 1)
7. 100 # 2x " 80 8. 3(g ' h) " 12
9. p2 # 2p " 9 10. C " (F # 32)
11. V " Bh 12. A " hb1%2
1%3
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Study Guide and Intervention (continued)
Writing Equations
NAME ______________________________________________ DATE ____________ PERIOD _____
3-13-1
ExampleExample
ExercisesExercises
Skills PracticeWriting Equations
NAME ______________________________________________ DATE ____________ PERIOD _____
3-13-1
© Glencoe/McGraw-Hill 139 Glencoe Algebra 1
Less
on
3-1
Translate each sentence into an equation.
1. Two added to three times a number m is the same as 18.
2. Twice a increased by the cube of a equals b.
3. Seven less than the sum of p and q is as much as 6.
4. The sum of x and its square is equal to y times z.
5. Four times the sum of f and g is identical to six times g.
Translate each sentence into a formula.
6. The perimeter P of a square equals four times the length of a side s.
7. The area A of a square is the length of a side s squared.
8. The perimeter P of a triangle is equal to the sum of the lengths of sides a, b, and c.
9. The area A of a circle is pi times the radius r squared.
10. The volume V of a rectangular prism equals the product of the length !, the width w,and the height h.
Translate each equation into a verbal sentence.
11. g ' 10 " 3g 12. 2p ' 4q " 20
13. 4(a ' b) " 9a 14. 8 # 6x " 4 ' 2x
15. ( f ' y) " f # 5 16. s2 # n2 " 2b
Write a problem based on the given information.
17. c " cost per pound of plain coffee beans 18. p " cost of dinnerc ' 3 " cost per pound of flavored coffee beans 0.15p " cost of a 15% tip2c ' (c ' 3) " 21 p ' 0.15p " 23
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© Glencoe/McGraw-Hill 140 Glencoe Algebra 1
Translate each sentence into an equation.
1. Fifty-three plus four times c is as much as 21.
2. The sum of five times h and twice g is equal to 23.
3. One fourth the sum of r and ten is identical to r minus 4.
4. Three plus the sum of the squares of w and x is 32.
Translate each sentence into a formula.
5. Degrees Kelvin K equals 273 plus degrees Celsius C.
6. The total cost C of gas is the price p per gallon times the number of gallons g.
7. The sum S of the measures of the angles of a polygon is equal to 180 times the differenceof the number of sides n and 2.
Translate each equation into a verbal sentence.
8. q # (4 ' p) " q 9. t ' 2 " t
10. 9(y2 ' x) " 18 11. 2(m # n) " v ' 7
Write a problem based on the given information.
12. a " cost of one adult’s ticket to zoo 13. c " regular cost of one airline ticketa # 4 " cost of one children’s ticket to zoo 0.20c " amount of 20% promotional discount2a ' 4(a # 4) " 38 3(c # 0.20c) " 330
14. GEOGRAPHY About 15% of all federally-owned land in the 48 contiguous states of theUnited States is in Nevada. If F represents the area of federally-owned land in thesestates, and N represents the portion in Nevada, write an equation for this situation.
FITNESS For Exercises 15–17, use the following information.Deanna and Pietra each go for walks around a lake a few times per week. Last week,Deanna walked 7 miles more than Pietra.15. If p represents the number of miles Pietra walked, write an equation that represents the
total number of miles T the two girls walked.
16. If Pietra walked 9 miles during the week, how many miles did Deanna walk?
17. If Pietra walked 11 miles during the week, how many miles did the two girls walktogether?
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Practice Writing Equations
NAME ______________________________________________ DATE ____________ PERIOD _____
3-13-1
Reading to Learn MathematicsWriting Equations
NAME ______________________________________________ DATE ____________ PERIOD _____
3-13-1
© Glencoe/McGraw-Hill 141 Glencoe Algebra 1
Less
on
3-1
Pre-Activity How are equations used to describe heights?
Read the introduction to Lesson 3-1 at the top of page 120 in your textbook.
Does the equation 305 # s " 154 also represent the situation? Explain.
Reading the Lesson
1. Translate each sentence into an equation.
a. Two times the sum of x and three minus four equals four times x.
b. The difference of k and 3 is two times k divided by five.
2. A 1 oz serving of chips has 140 calories. There are about 14 servings of chips in a bag.How many calories are there in a bag of chips? Write what your solution would be as youuse each step in the Four-Step Problem-Solving Plan.
Explore What do you know?
What do you want to know?
Plan Write an equation.
Solve Solve the problem.
Examine Does your answer make sense?
Helping You Remember
3. If you cannot remember all the steps of the Four-Step Problem-Solving Plan, try toremember the first letters of the first word in each step. Write those letters here withtheir associated words.
© Glencoe/McGraw-Hill 142 Glencoe Algebra 1
Rep-TilesA rep-tile is a figure that can be subdivided into smaller copies of itself. The large figure is similar to the small ones and the small figures are allcongruent.
Show that each figure is a rep-tile by subdividing it into four smaller and similar figures.
1. 2. 3.
4. 5. 6.
Subdivide each rep-tile into nine smaller and similar figures.
7. 8.
9. 10.
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
3-13-1
Study Guide and InterventionSolving Equations by Using Addition and Subtraction
NAME ______________________________________________ DATE ____________ PERIOD _____
3-23-2
© Glencoe/McGraw-Hill 143 Glencoe Algebra 1
Less
on
3-2
Solve Using Addition If the same number is added to each side of an equation, theresulting equation is equivalent to the original one. In general if the original equationinvolves subtraction, this property will help you solve the equation.
Addition Property of Equality For any numbers a, b, and c, if a " b, then a ' c " b ' c.
Solve m ! 32 " 18.
m # 32 " 18 Original equation
m # 32 ' 32 " 18 ' 32 Add 32 to each side.
m " 50 Simplify.
The solution is 50.
Solve !18 " p !12.
#18 " p #12 Original equation
#18 ' 12 " p #12 ' 12 Add 12 to each side.
p " #6 Simplify.
The solution is #6.
Example 1Example 1 Example 2Example 2
ExercisesExercises
Solve each equation. Then check your solution.
1. h # 3 " #2 2. m # 8 " #12 3. p # 5 " 15
4. 20 " y # 8 5. k # 0.5 " 2.3 6. w # "
7. h # 18 " #17 8. #12 " #24 ' k 9. j # 0.2 " 1.8
10. b # 40 " #40 11. m # (#12) " 10 12. w # "
Write an equation for each problem. Then solve the equation and check thesolution.
13. Twelve subtracted from a number equals 25. Find the number.
14. What number decreased by 52 equals #12?
15. Fifty subtracted from a number equals eighty. Find the number.
16. What number minus one-half is equal to negative one-half ?
17. The difference of a number and eight is equal to 14. What is the number?
18. A number decreased by fourteen is equal to eighteen. What is the number?
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© Glencoe/McGraw-Hill 144 Glencoe Algebra 1
Solve Using Subtraction If the same number is subtracted from each side of anequation, the resulting equation is equivalent to the original one. In general if the originalequation involves addition, this property will help you solve the equation.
Subtraction Property of Equality For any numbers a, b, and c, if a " b, then a # c " b # c.
Solve 22 # p " !12.
22 ' p " #12 Original equation
22 ' p # 22 " #12 # 22 Subtract 22 from each side.
p " #34 Simplify.
The solution is #34.
Solve each equation. Then check your solution.
1. x ' 12 " 6 2. z ' 2 " #13 3. #17 " b ' 4
4. s ' (#9) " 7 5. #3.2 " ! ' (#0.2) 6. # ' x "
7. 19 ' h " #4 8. #12 " k ' 24 9. j ' 1.2 " 2.8
10. b ' 80 " #80 11. m ' (#8) " 2 12. w ' "
Write an equation for each problem. Then solve the equation and check thesolution.
13. Twelve added to a number equals 18. Find the number.
14. What number increased by 20 equals #10?
15. The sum of a number and fifty equals eighty. Find the number.
16. What number plus one-half is equal to four?
17. The sum of a number and 3 is equal to #15. What is the number?
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Study Guide and Intervention (continued)
Solving Equations by Using Addition and Subtraction
NAME ______________________________________________ DATE ____________ PERIOD _____
3-23-2
ExampleExample
ExercisesExercises
Skills PracticeSolving Equations by Using Addition and Subtraction
NAME ______________________________________________ DATE ____________ PERIOD _____
3-23-2
© Glencoe/McGraw-Hill 145 Glencoe Algebra 1
Less
on
3-2
Solve each equation. Then check your solution.
1. y # 7 " 8 2. w ' 14 " #8
3. p # 4 " 6 4. #13 " 5 ' x
5. 98 " b ' 34 6. y # 32 " #1
7. s ' (#28) " 0 8. y ' (#10) " 6
9. #1 " s ' (#19) 10. j # (#17) " 36
11. 14 " d ' (#10) 12. u ' (#5) " #15
13. 11 " #16 ' y 14. c # (#3) " 100
15. 47 " w # (#8) 16. x # (#74) " #22
17. 4 # (#h) " 68 18. #56 " 20 # (#e)
Write an equation for each problem. Then solve the equation and check yoursolution.
19. A number decreased by 14 is #46. Find the number.
20. Thirteen subtracted from a number is #5. Find the number.
21. The sum of a number and 67 is equal to #34. Find the number.
22. What number minus 28 equals #2?
23. A number plus #73 is equal to 27. What is the number?
24. A number plus #17 equals #1. Find the number.
25. What number less 5 is equal to #39?
© Glencoe/McGraw-Hill 146 Glencoe Algebra 1
Solve each equation. Then check your solution.
1. d # 8 " 17 2. v ' 12 " #5 3. b # 2 " #11
4. #16 " s ' 71 5. 29 " a # 76 6. #14 ' y " #2
7. 8 # (#c) " 1 8. 78 ' r " #15 9. f ' (#3) " #9
10. 4.2 " n ' 7.3 11. w ' 1.9 " #2.5 12. 4.6 # (#b) " #0.4
13. y # (#1.5) " 0.5 14. a # 0.13 " #0.58 15. k ' (#4.21) " #19
16. r ' " 17. ' q " 18. " h '
19. ' x " # 20. y ' " 21. # # (#n) " #
Write an equation for each problem. Then solve the equation and check yoursolution.
22. What number minus 9 is equal to #18?
23. A number plus 15 equals #12. What is the number?
24. The sum of a number and #3 is equal to #91. Find the number.
25. Negative seventeen equals 63 plus a number. What is the number?
26. The sum of negative 14, a number, and 6 is #5. What is the number?
27. What number plus one half is equal to three eighths?
HISTORY For Exercises 28 and 29, use the following information.
Galileo Galilei was born in 1564. Many years later, in 1642, Sir Isaac Newton was born.
28. Write an addition equation to represent the situation.
29. How many years after Galileo was born was Isaac Newton born?
HURRICANES For Exercises 30 and 31, use the following information.
The day after a hurricane, the barometric pressure in a coastal town has risen to 29.7 inches of mercury, which is 2.9 inches of mercury higher than the pressure when theeye of the hurricane passed over.
30. Write an addition equation to represent the situation.
31. What was the barometric pressure when the eye passed over?
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Practice Solving Equations by Using Addition and Subtraction
NAME ______________________________________________ DATE ____________ PERIOD _____
3-23-2
Reading to Learn MathematicsSolving Equations by Using Addition and Subtraction
NAME ______________________________________________ DATE ____________ PERIOD _____
3-23-2
© Glencoe/McGraw-Hill 147 Glencoe Algebra 1
Less
on
3-2
Pre-Activity How can equations be used to compare data?
Read the introduction to Lesson 3-2 at the top of page 128 in your textbook.
In the equation m # 66 " 5, the number 5 represents
and the number 66 represents
Reading the Lesson
1. To solve x ' 17 " 46 using the Subtraction Property of Equality, you would subtract from each side.
2. To solve y # 9 " #30 using the Addition Property of Equality, you would add to each side.
3. Write an equation that you could solve by subtracting 32 from each side.
4. A student used the Subtraction Property of Equality to solve an equation. Explain why itwould also be possible to use the Addition Property of Equality to solve the equation.
Helping You Remember
5. Explain how you decide whether to use the Addition Property or the SubtractionProperty of Equality to solve an equation.
© Glencoe/McGraw-Hill 148 Glencoe Algebra 1
Counting-Off PuzzlesSolve each puzzle.
1. Twenty-five people are standing in a circle.Starting with person 1, they count off from 1 to 7 and then start over with 1. Each person who says “7” drops out of the circle.Who is the last person left?
2. Forty people stand in a circle. They count off so that every third person drops out. Which two people are the last ones left?
3. Only half of the 30 students in Sharon’s class can go on a field trip. Sharon arranges the boys and girls as shown. They count off from 1 to 9 and every ninthperson drops out until only 15 people are left. Who gets to go on the field trip.
A group of people stand in a circle and count off 1, 2, 1, 2, 1 and so on. Every second person drops out. Person number 1 is the last person left.
4. Draw a diagram to show why the number of people in the circle must be even. Then, explain your answer.
5. When the count returns to person number 1 for the first time, how many people have dropped out?
6. Find the number of people in the circle if the number is between 10 and 20. Do the same if the number is between 30 and 40. What can you conclude about the original number of people?
G
GG
G
G G GG
GG
G
GGG
G B
B
B B B
BBBBBB
BB
B
B1
23 4 5 6 7 8 9 10
1112
13
14
1516
171819202122232425
2627
28
29
30
1 2 3 45
6
7
8
9
10
11
1213
1415161718
19
20
21
22
23
2425
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
3-23-2
Study Guide and InterventionSolving Equations by Using Multiplication and Division
NAME ______________________________________________ DATE ____________ PERIOD _____
3-33-3
© Glencoe/McGraw-Hill 149 Glencoe Algebra 1
Less
on
3-3
Solve Using Multiplication If each side of an equation is multiplied by the samenumber, the resulting equation is equivalent to the given one. You can use the property tosolve equations involving multiplication and division.
Multiplication Property of Equality For any numbers a, b, and c, if a " b, then ac " bc.
Solve 3 p " 1 .
3 p " 1 Original equation
p " Rewrite each mixed number as animproper fraction.
" p# " " # Multiply each side by .
p " Simplify.
The solution is .3%7
3%7
2%7
3%2
2%7
7%2
2%7
3%2
7%2
1%2
1%2
1$2
1$2 Solve ! n " 16.
# n " 16 Original equation
#4"# n# " #4(16) Multiply each side by #4.
n " #64 Simplify.
The solution is #64.
1%4
1%4
1$4
Example 1Example 1 Example 2Example 2
ExercisesExercises
Solve each equation. Then check your solution.
1. " #2 2. m " 6 3. p "
4. 5 " 5. # k " #2.5 6. # "
7. #1 h " 4 8. #12 " # k 9. "
10. #3 b " 5 11. m " 10 12. " #
Write an equation for each problem. Then solve the equation.
13. One-fifth of a number equals 25. Find the number.
14. What number divided by 2 equals #18?
15. A number divided by eight equals 3. Find the number.
16. One and a half times a number equals 6. Find the number.
1%4
p%5
7%10
1%3
2%5
j%3
3%2
1%2
5%8
m%8
1%4
y%12
3%5
1%5
1%8
h%3
© Glencoe/McGraw-Hill 150 Glencoe Algebra 1
Solve Using Division To solve equations with multiplication and division, you can alsouse the Division Property of Equality. If each side of an equation is divided by the samenumber, the resulting equation is true.
Division Property of Equality For any numbers a, b, and c, with c ( 0, if a " b, then " .b%c
a%c
Study Guide and Intervention (continued)
Solving Equations by Using Multiplication and Division
NAME ______________________________________________ DATE ____________ PERIOD _____
3-33-3
Solve 8n " 64.
8n " 64 Original equation
" Divide each side by 8.
n " 8 Simplify.
The solution is 8.
64%8
8n%8
Solve !5n " 60.
#5n " 60 Original equation
" Divide each side by #5.
n " #12 Simplify.
The solution is #12.
60%#5
#5n%#5
Example 1Example 1 Example 2Example 2
ExercisesExercises
Solve each equation. Then check your solution.
1. 3h " #42 2. 8m " 16 3. #3t " 51
4. #3r " #24 5. 8k " #64 6. #2m " 16
7. 12h " 4 8. #2.4p " 7.2 9. 0.5j " 5
10. #25 " 5m 11. 6m " 15 12. #1.5p " #75
Write an equation for each problem. Then solve the equation.
13. Four times a number equals 64. Find the number.
14. What number multiplied by #4 equals #16?
15. A number times eight equals #36. Find the number.
Skills PracticeSolving Equations by Using Multiplication and Division
NAME ______________________________________________ DATE ____________ PERIOD _____
3-33-3
© Glencoe/McGraw-Hill 151 Glencoe Algebra 1
Less
on
3-3
Solve each equation. Then check your solution.
1. 12z " 108 2. #7t " 49
3. 18e " #216 4. #22 " 11v
5. #6d " #42 6. 96 " #24a
7. " 16 8. " 9
9. #84 " 10. # " #13
11. " #13 12. 31 " # n
13. #6 " z 14. q " #4
15. p " #10 16. "
17. #0.4b " 5.2 18. 1.6m " #4
Write an equation for each problem. Then solve the equation.
19. The opposite of a number is #9. What is the number?
20. Fourteen times a number is #42. Find the number.
21. Eight times a number equals 128. What is the number?
22. Negative twelve times a number equals #132. Find the number.
23. Negative eighteen times a number is #54. What is the number?
24. One sixth of a number is #17. Find the number.
25. Negative three fifths of a number is #15. What is the number?
2%5
a%10
5%9
2%7
2%3
1%6
t%4
d%7
d%3
a%16
c%4
© Glencoe/McGraw-Hill 152 Glencoe Algebra 1
Solve each equation. Then check your solution.
1. 8j " 96 2. #13z " #39 3. #180 " 15m
4. 243 " 27c 5. " #8 6. # " #8
7. " 8. " 9. "
10. #1 " # t 11. # w " #9 12. # s " 4
13. #3x " 14. a " 15. h "
16. 5n " 17. 2.5k " 20 18. #3.4e " #3.74
19. #1.7b " 2.21 20. 0.26p " 0.104 21. 4.2q " #3.36
Write an equation for each problem. Then solve the equation.
22. Negative nine times a number equals #117. Find the number.
23. Negative one eighth of a number is # . What is the number?
24. Five sixths of a number is # . Find the number.
25. 2.7 times a number equals 8.37. What is the number?
26. One and one fourth times a number is one and one third. What is the number?
27. PUBLISHING Two units of measure used in publishing are the pica and the point. A picais one sixth of an inch. There are 12 points in a pica, so Points " 12 · Picas. How manypicas are equivalent to 108 points?
ROLLER COASTERS For Exercises 28 and 29, use the following information.
Superman the Escape in California is the fastest roller coaster in the world. Riders fall 415 feet in 7 seconds. Speeds reach a maximum of 100 miles per hour.
28. If x represents the average rate of fall of the roller coaster, write an expression torepresent the situation (Hint: Use the distance formula d " rt.)
29. What is the average rate that riders fall in feet per second?
5%9
3%4
11%4
11%6
5%3
4%3
8%5
3%2
3%15
3%8
4%7
1%6
q%24
2%9
g%27
4%5
a%15
j%12
y%9
Practice Solving Equations by Using Multiplication and Division
NAME ______________________________________________ DATE ____________ PERIOD _____
3-33-3
Reading to Learn MathematicsSolving Equations by Using Multiplication and Division
NAME ______________________________________________ DATE ____________ PERIOD _____
3-33-3
© Glencoe/McGraw-Hill 153 Glencoe Algebra 1
Less
on
3-3
Pre-Activity How can equations be used to find how long it takes light to reachEarth?
Read the introduction to Lesson 3-3 at the top of page 135 in your textbook.
• In the equation d " rt, shown in the introduction, what number is usedfor r? for d?
• What equation could you use to find the time it takes light to reach Earthfrom the farthest star in the Big Dipper?
Reading the Lesson
Complete the sentence after each equation to tell how you would solve theequation.
1. " 16 each side by .
2. 5x " 125 each side by , or multiply each side by .
3. #8k " 96 Divide each side by , or multiply each side by
4. Explain how rewriting 4 x " 2 as x " helps you solve the equation.
Helping You Remember
5. One way to remember something is to explain it to someone else. Write how you would explain to a classmate how to solve the equation x " 12.2
%3
17%8
13%3
1%8
1%3
x%7
© Glencoe/McGraw-Hill 154 Glencoe Algebra 1
Dissection Puzzles: Make the SquareIn a dissection puzzle, you are to cut apart one figure using onlystraight cuts and then rearrange the pieces to make a new figure.Usually the puzzle-solver must figure out where to make the givennumber of cuts. However, for these puzzles, the cut lines are shown.You must discover how to rearrange the pieces.
Cut apart each figure. Then rearrange the pieces to form a square.
1.
2.
3.
4. Hint: Cut one of the triangles into two pieces to make this square.
A AA A
A
2x 2x 2x
x
A AA A
B
2x 2x x
x
A
C
B
D
A
BB
BB
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
3-33-3
Study Guide and InterventionSolving Multi-Step Equations
NAME ______________________________________________ DATE ____________ PERIOD _____
3-43-4
© Glencoe/McGraw-Hill 155 Glencoe Algebra 1
Less
on
3-4
Work Backward Working backward is one of many problem-solving strategies thatyou can use to solve problems. To work backward, start with the result given at the end of aproblem and undo each step to arrive at the beginning number.
A number is dividedby 2, and then 8 is subtracted fromthe quotient. The result is 16. Whatis the number?
Solve the problem by working backward.The final number is 16. Undosubtracting 8 by adding 8 to get 24. Toundo dividing 24 by 2, multiply 24 by 2to get 48.The original number is 48.
A bacteria culture doubleseach half hour. After 3 hours, there are6400 bacteria. How many bacteria werethere to begin with?
Solve the problem by working backward.The bacteria have grown for 3 hours. Since thereare 2 one-half hour periods in one hour, in 3 hoursthere are 6 one-half hour periods. Since thebacteria culture has grown for 6 time periods, ithas doubled 6 times. Undo the doubling byhalving the number of bacteria 6 times.
6,400 ! ! ! ! ! ! " 6,400 !
" 100
There were 100 bacteria to begin with.
1%64
1%2
1%2
1%2
1%2
1%2
1%2
Example 1Example 1 Example 2Example 2
ExercisesExercises
Solve each problem by working backward.
1. A number is divided by 3, and then 4 is added to the quotient. The result is 8. Find thenumber.
2. A number is multiplied by 5, and then 3 is subtracted from the product. The result is 12.Find the number.
3. Eight is subtracted from a number, and then the difference is multiplied by 2. The resultis 24. Find the number.
4. Three times a number plus 3 is 24. Find the number.
5. CAR RENTAL Angela rented a car for $29.99 a day plus a one-time insurance cost of$5.00. Her bill was $124.96. For how many days did she rent the car?
6. MONEY Mike withdrew an amount of money from his bank account. He spent onefourth for gasoline and had $90 left. How much money did he withdraw?
7. TELEVISIONS In 1999, 68% of households with TV’s subscribed to cable TV. If 8,000 moresubscribers are added to the number of households with cable, the total number ofhouseholds with cable TV would be 67,600,000. How many households were there withTV in 1999? Source: World Almanac
© Glencoe/McGraw-Hill 156 Glencoe Algebra 1
Solve Multi-Step Equations To solve equations with more than one operation, oftencalled multi-step equations, undo operations by working backward. Reverse the usualorder of operations as you work.
Solve 5x # 3 " 23.
5x ' 3 " 23 Original equation.
5x ' 3 # 3 " 23 # 3 Subtract 3 from each side.
5x " 20 Simplify.
" Divide each side by 5.
x " 4 Simplify.
Solve each equation. Then check your solution.
1. 5x ' 2 " 27 2. 6x ' 9 " 27 3. 5x ' 16 " 51
4. 14n # 8 " 34 5. 0.6x # 1.5 " 1.8 6. p # 4 " 10
7. 16 " 8. 8 ' " 13 9. ' 3 " #13
10. " 10 11. 0.2x # 8 " #2 12. 3.2y # 1.8 " 3
13. #4 " 14. 8 " #12 ' 15. 0 " 10y # 40
Write an equation and solve each problem.
16. Find three consecutive integers whose sum is 96.
17. Find two consecutive odd integers whose sum is 176.
18. Find three consecutive integers whose sum is #93.
k%#4
7x # (#1)%%
#8
4b ' 8%
#2
g%#5
3n%12
d # 12%14
7%8
20%5
5x%5
Study Guide and Intervention (continued)
Solving Multi-Step Equations
NAME ______________________________________________ DATE ____________ PERIOD _____
3-43-4
ExampleExample
ExercisesExercises
Skills PracticeSolving Multi-Step Equations
NAME ______________________________________________ DATE ____________ PERIOD _____
3-43-4
© Glencoe/McGraw-Hill 157 Glencoe Algebra 1
Less
on
3-4
Solve each problem by working backward.
1. A number is divided by 2, and then the quotient is added to 8. The result is 33. Find thenumber.
2. Two is subtracted from a number, and then the difference is divided by 3. The result is30. Find the number.
3. A number is multiplied by 2, and then the product is added to 9. The result is 49. Whatis the number?
4. ALLOWANCE After Ricardo received his allowance for the week, he went to the mallwith some friends. He spent half of his allowance on a new paperback book. Then hebought himself a snack for $1.25. When he arrived home, he had $5.00 left. How muchwas his allowance?
Solve each equation. Then check your solution.
5. 5x ' 3 " 23 6. 4 " 3a # 14 7. 2y ' 5 " 19
8. 6 ' 5c " #29 9. 8 # 5w " #37 10. 18 # 4v " 42
11. # 8 " #2 12. 5 ' " 1 13. # # 4 " 13
14. # ' 12 " #7 15. # 2 " 9 16. ' 3 " #1
17. q # 7 " 8 18. g ' 6 " #12 19. z # 8 " #3
20. m ' 2 " 6 21. " 3 22. " 2
Write an equation and solve each problem.
23. Twice a number plus four equals 6. What is the number?
24. Sixteen is seven plus three times a number. Find the number.
25. Find two consecutive integers whose sum is 35.
26. Find three consecutive integers whose sum is 36.
b ' 1%3
c # 5%4
4%5
5%2
2%3
3%4
w%7
a%5
d%6
h%3
x%4
n%3
© Glencoe/McGraw-Hill 158 Glencoe Algebra 1
Solve each problem by working backward.
1. Three is added to a number, and then the sum is multiplied by 4. The result is 16. Findthe number.
2. A number is divided by 4, and the quotient is added to 3. The result is 24. What is thenumber?
3. Two is subtracted from a number, and then the difference is multiplied by 5. The resultis 30. Find the number.
4. BIRD WATCHING While Michelle sat observing birds at a bird feeder, one fourth of thebirds flew away when they were startled by a noise. Two birds left the feeder to go toanother stationed a few feet away. Three more birds flew into the branches of a nearbytree. Four birds remained at the feeder. How many birds were at the feeder initially?
Solve each equation. Then check your solution.
5. #12n # 19 " 77 6. 17 ' 3f " 14 7. 15t ' 4 " 49
8. ' 6 " 2 9. ' 3 " 15 10. # 6 " #2
11. y # " 12. #32 # f " #17 13. 8 # k " #4
14. " 1 15. " #9 16. " 16
17. # 0.5 " 2.5 18. 2.5g ' 0.45 " 0.95 19. 0.4m # 0.7 " 0.22
Write an equation and solve each problem.
20. Seven less than four times a number equals 13. What is the number?
21. Find two consecutive odd integers whose sum is 116.
22. Find two consecutive even integers whose sum is 126.
23. Find three consecutive odd integers whose sum is 117.
24. COIN COLLECTING Jung has a total of 92 coins in his coin collection. This is 8 morethan three times the number of quarters in the collection. How many quarters does Junghave in his collection?
x%7
3k # 7%5
15 # a%3
r ' 13%12
3%8
3%5
7%8
1%8
1%2
b%3
d%#4
u%5
Practice Solving Multi-Step Equations
NAME ______________________________________________ DATE ____________ PERIOD _____
3-43-4
Reading to Learn MathematicsSolving Multi-Step Equations
NAME ______________________________________________ DATE ____________ PERIOD _____
3-43-4
© Glencoe/McGraw-Hill 159 Glencoe Algebra 1
Less
on
3-4
Pre-Activity How can equations be used to estimate the age of an animal?
Read the introduction to Lesson 3-4 at the top of page 142 in your textbook.
• Write the equation 8 ' 12a " 124 in words.
• How many operations are involved in the equation?
Reading the Lesson
1. What does the phrase undo the operations mean to you? Give an example.
2. a. If we undo operations in reverse of the order of operations, what operations do we dofirst?
b. What operations do we do last?
3. Suppose you want to solve " 6.
a. What is the grouping symbol in the equation " 6?
b. What is the first step in solving the equation?
c. What is the next step in solving the equation?
4. Write an equation for the problem below.
Seven times k minus five equals negative forty-seven
Helping You Remember
5. Explain why working backward is a useful strategy for solving equations.
x ' 3%5
x ' 3%5
© Glencoe/McGraw-Hill 160 Glencoe Algebra 1
Consecutive Integer ProblemsMany types of problems and puzzles involve the idea of consecutiveintegers. Knowing how to represent these integers algebraically canhelp to solve the problem.
Find four consecutive odd integers whose sum is !80.
An odd integer can be written as 2n ' 1, where n is any integer.If 2n + 1 is the first odd integer, then add 2 to get the next largest oddinteger, and so on.Now write an equation to solve this problem.(2n ' 1) ' (2n ' 3) ' (2n ' 5) ' (2n ' 7) " #80
Write an equation for each problem. Then solve.
1. Complete the solution to the problem in the example.
2. Find three consecutive even integers whose sum is 132.
3. Find two consecutive integers whose sum is 19.
4. Find two consecutive integers whose sum is 100.
5. The lesser of two consecutive even integers is 10 more than one-half the greater. Find the integers.
6. The greater of two consecutive even integers is 6 less than three times the lesser. Find the integers.
7. Find four consecutive integers such that twice the sum of the two greater integers exceeds three times the first by 91.
8. Find a set of four consecutive positive integers such that the greatest integer in the set is twice the least integer in the set.
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
3-43-4
ExampleExample
ExercisesExercises
Study Guide and InterventionSolving Equations with the Variable on Each Side
NAME ______________________________________________ DATE ____________ PERIOD _____
3-53-5
© Glencoe/McGraw-Hill 161 Glencoe Algebra 1
Less
on
3-5
Variables on Each Side To solve an equation with the same variable on each side,first use the Addition or the Subtraction Property of Equality to write an equivalentequation that has the variable on just one side of the equation. Then solve the equation.
Solve 5y ! 8 " 3y # 12.
5y # 8 " 3y ' 125y # 8 # 3y " 3y ' 12 # 3y
2y # 8 " 122y # 8 ' 8 " 12 ' 8
2y " 20
"
y " 10
The solution is 10.
20%2
2y%2
Solve !11 ! 3y " 8y # 1.
#11 # 3y " 8y ' 1#11 # 3y ' 3y " 8y ' 1 ' 3y
#11 " 11y ' 1#11 # 1 " 11y ' 1 # 1
#12 " 11y
"
#1 " y
The solution is #1 .1%11
1%11
11y%11
#12%11
Example 1Example 1 Example 2Example 2
ExercisesExercises
Solve each equation. Then check your solution.
1. 6 # b " 5b ' 30 2. 5y # 2y " 3y ' 2 3. 5x ' 2 " 2x # 10
4. 4n # 8 " 3n ' 2 5. 1.2x ' 4.3 " 2.1 # x 6. 4.4s ' 6.2 " 8.8s # 1.8
7. b ' 4 " b ' 88 8. k # 5 " k # 1 9. 8 # 5p " 4p # 1
10. 4b # 8 " 10 # 2b 11. 0.2x # 8 " #2 # x 12. 3y # 1.8 " 3y # 1.8
13. #4 # 3x " 7x # 6 14. 8 ' 4k " #10 ' k 15. 20 # a " 10a # 2
16. n ' 8 " n ' 2 17. y # 8 " 9 # y 18. #4r ' 5 " 5 # 4r
19. #4 # 3x " 6x # 6 20. 18 # 4k " #10 #4k 21. 12 ' 2y " 10y # 12
3%5
2%5
1%2
2%3
1%4
3%4
1%8
1%2
© Glencoe/McGraw-Hill 162 Glencoe Algebra 1
Grouping Symbols When solving equations that contain grouping symbols, first usethe Distributive Property to eliminate grouping symbols. Then solve.
Solve 4(2a ! 1) " !10(a ! 5).
4(2a # 1) " #10(a # 5) Original equation
8a # 4 " #10a ' 50 Distributive Property
8a # 4 ' 10a " #10a ' 50 ' 10a Add 10a to each side.
18a # 4 " 50 Simplify.
18a # 4 ' 4 " 50 ' 4 Add 4 to each side.
18a " 54 Simplify.
" Divide each side by 18.
a " 3 Simplify.
The solution is 3.
Solve each equation. Then check your solution.
1. #3(x ' 5) " 3(x # 1) 2. 2(7 ' 3t) " #t 3. 3(a ' 1) # 5 " 3a # 2
4. 75 # 9g " 5(#4 ' 2g) 5. 5(f ' 2) " 2(3 # f ) 6. 4(p ' 3) " 36
7. 18 " 3(2c ' 2) 8. 3(d # 8) " 3d 9. 5(p ' 3) ' 9 " 3(p # 2) ' 6
10. 4(b # 2) " 2(5 # b) 11. 1.2(x # 2) " 2 # x 12. "
13. " 14. 2(4 ' 2k) ' 10 " k 15. 2(w # 1) ' 4 " 4(w ' 1)
16. 6(n # 1) " 2(2n ' 4) 17. 2[2 ' 3( y # 1)] " 22 18. #4(r ' 2) " 4(2 # 4r)
19. #3(x # 8) " 24 20. 4(4 # 4k) " #10 #16k 21. 6(2 # 2y) " 5(2y # 2)
2a ' 5%3
a # 8%12
#y %8
3 ' y%4
54%18
18a%18
Study Guide and Intervention (continued)
Solving Equations with the Variable on Each Side
NAME ______________________________________________ DATE ____________ PERIOD _____
3-53-5
ExampleExample
ExercisesExercises
Skills PracticeSolving Equations with the Variable on Each Side
NAME ______________________________________________ DATE ____________ PERIOD _____
3-53-5
© Glencoe/McGraw-Hill 163 Glencoe Algebra 1
Less
on
3-5
Justify each step.
1. 4k # 3 " 2k ' 54k # 3 # 2k " 2k ' 5 # 2k a.
2k # 3 " 5 b.
2k # 3 ' 3 " 5 ' 3 c.
2k " 8 d.
" e.
k " 4 f.
2. 2(8u ' 2) " 3(2u # 7)16u ' 4 " 6u # 21 a.
16u ' 4 # 6u " 6u # 21 # 6u b.
10u ' 4 " #21 c.
10u ' 4 # 4 " #21 # 4 d.
10u " #25 e.
" f.
u " #2.5 g.
Solve each equation. Then check your solution.
3. 2m ' 12 " 3m # 31 4. 2h # 8 " h ' 17
5. 7a # 3 " 3 # 2a 6. 4n # 12 " 12 # 4n
7. 4x # 9 " 7x ' 12 8. #6y # 3 " 3 # 6y
9. 5 ' 3r " 5r # 19 10. #9 ' 8k " 7 ' 4k
11. 8q ' 12 " 4(3 ' 2q) 12. 3(5j ' 2) " 2(3j # 6)
13. 6(#3v ' 1) " 5(#2v # 2) 14. #7(2b # 4) " 5(#2b ' 6)
15. 3(8 # 3t) " 5(2 ' t) 16. 2(3u ' 7) " #4(3 # 2u)
17. 8(2f # 2) " 7(3f ' 2) 18. 5(#6 # 3d) " 3(8 ' 7d)
19. 6(w # 1) " 3(3w ' 5) 20. 7(#3y ' 2) " 8(3y # 2)
21. v # 6 " 6 # v 22. # x " x '7%2
7%8
5%8
1%2
2%3
2%3
#25%10
10u%10
8%2
2k%2
© Glencoe/McGraw-Hill 164 Glencoe Algebra 1
Solve each equation. Then check your solution.
1. 5x # 3 " 13 # 3x 2. #4c # 11 " 4c ' 21
3. 1 # s " 6 # 6s 4. 14 ' 5n " #4n ' 17
5. k # 3 " 2 # k 6. (6 # z) " z
7. 3(#2 # 3x) " #9x # 4 8. 4(4 # w) " 3(2w ' 2)
9. 9(4b # 1) " 2(9b ' 3) 10. 3(6 ' 5y) " 2(#5 ' 4y)
11. #5x # 10 " 2 # (x ' 4) 12. 6 ' 2(3j # 2) " 4(1 ' j)
13. t # t " 3 ' t 14. 1.4f ' 1.1 " 8.3 # f
15. x # " x ' 16. 2 # z " z ' 9
17. (3g # 2) " 18. (c ' 1) " (3c # 5)
19. (5 # 2h) " 20. (2m # 16) " (2m ' 4)
21. 3(d # 8) # 5 " 9(d ' 2) ' 1 22. 2(a # 8) ' 7 " 5(a ' 2) # 3a # 19
23. Two thirds of a number reduced by 11 is equal to 4 more than the number. Find thenumber.
24. Five times the sum of a number and 3 is the same as 3 multiplied by 1 less than twicethe number. What is the number?
25. NUMBER THEORY Tripling the greater of two consecutive even integers gives the sameresult as subtracting 10 from the lesser even integer. What are the integers?
26. GEOMETRY The formula for the perimeter of a rectangle is P " 2! ' 2w, where ! isthe length and w is the width. A rectangle has a perimeter of 24 inches. Find itsdimensions if its length is 3 inches greater than its width.
1%3
1%9
h%2
1%4
1%6
1%3
g%6
1%2
1%8
3%4
5%6
1%2
1%6
2%3
3%2
5%2
1%2
3%4
1%2
Practice Solving Equations with the Variable on Each Side
NAME ______________________________________________ DATE ____________ PERIOD _____
3-53-5
Reading to Learn MathematicsSolving Equations with the Variable on Each Side
NAME ______________________________________________ DATE ____________ PERIOD _____
3-53-5
© Glencoe/McGraw-Hill 165 Glencoe Algebra 1
Less
on
3-5
Pre-Activity How can an equation be used to determine when two populationsare equal?
Read the introduction to Lesson 3-5 at the top of page 149 in your textbook.
In the equation 12 ' 7.6x " 6 ' 8x, what do 7.6x and 8x represent?
Reading the Lesson
1. Suppose you want to help a friend solve 6k ' 7 " 3k # 8. What would you advise her todo first? Why?
2. When solving 2(3x # 4)" 3(x ' 5), why is it helpful first to use the Distributive Propertyto remove the grouping symbols?
3. On a quiz, Jason solved three equations. His teacher said all the work was correct, butshe asked him to write short sentences to tell what the solutions were. In what follows,you see the last equation in his work for each equation. Write sentences to describe thesolutions.
a. x " #4
b. 6m " 6m
c. 12 " 37
4. In Question 3, one of the equations Jason solved was an identity. Which equation was it?Explain how you know.
Helping You Remember
5. An equation with variables is an identity when the equation is always true. In otherwords, the expressions on the left and right sides always have the same value. Look upthe word identity in the dictionary. Write all the definitions that are similar to themathematical definition.
© Glencoe/McGraw-Hill 166 Glencoe Algebra 1
IdentitiesAn equation that is true for every value of the variable is called anidentity. When you try to solve an identity, you end up with astatement that is always true. Here is an example.
Solve 8 ! (5 ! 6x) " 3(1 # 2x).
8 # (5 # 6x) " 3(1 ' 2x)
8 # 5 # (#6x) " 3(1 ' 2x)
8 # 5 ' 6x " 3 ' 6x
3 ' 6x " 3 ' 6x
State whether each equation is an identity. If it is not, find its solution.
1. 2(2 # 3x) " 3(3 ' x) ' 4 2. 5(m ' 1) ' 6 " 3(4 ' m) ' (2m # 1)
3. (5t ' 9) # (3t # 13) " 2(11 ' t) 4. 14 # (6 # 3c) " 4c # c
5. 3y # 2( y ' 19) " 9y # 3(9 # y) 6. 3(3h # 1) " 4(h ' 3)
7. Use the true equation 3x # 2 " 3x # 2 to create an identity of your own.
8. Use the false equation 1 " 2 to create an equation with no solution.
9. Create an equation whose solution is x " 3.
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
3-53-5
ExampleExample
ExercisesExercises
Study Guide and InterventionRatios and Proportions
NAME ______________________________________________ DATE ____________ PERIOD _____
3-63-6
© Glencoe/McGraw-Hill 167 Glencoe Algebra 1
Less
on
3-6
Ratios and Proportions A ratio is a comparison of two numbers by division. The ratio
of x to y can be expressed as x to y, x:y or . Ratios are usually expressed in simplest form.
An equation stating that two ratios are equal is called a proportion. To determine whethertwo ratios form a proportion, express both ratios in simplest form or check cross products.
x%y
Determine whether the
ratios and form a proportion.
" when expressed in simplest form.
" when expressed in simplest form.
The ratios and form a proportion
because they are equal when expressed insimplest form.
12%18
24%36
2%3
12%18
2%3
24%36
12$18
24$36
Use cross products to
determine whether and form aproportion.
! Write the proportion.
10(45) ! 18(25) Cross products
450 " 450 Simplify.
The cross products are equal, so " .
Since the ratios are equal, they form aproportion.
25%45
10%18
25%45
10%18
25$45
10$18
Example 1Example 1 Example 2Example 2
ExercisesExercises
Use cross products to determine whether each pair of ratios forms a proportion.
1. , 2. , 3. ,
4. , 5. , 6. ,
7. , 8. , 9. ,
10. 2:3, 20:30 11. 5 to 9, 25 to 45 12. ,
13. 5:5, 30:20 14. 18 to 24, 50 to 75 15. 100:75, 44:33
16. , 17. , 18. , 0.45%0.9
0.1%0.2
6%8
1.5%2
1%20
0.05%1
9%8
72%64
20%30
14%21
9%12
15%20
5%100
0.1%2
12%27
4%9
3%16
12%32
15%20
25%36
25%49
10%20
10%15
5%8
16%32
1%2
© Glencoe/McGraw-Hill 168 Glencoe Algebra 1
Solve Proportions If a proportion involves a variable, you can use cross products to solve
the proportion. In the proportion " , x and 13 are called extremes and 5 and 10 are
called means. In a proportion, the product of the extremes is equal to the product of the means.
Means-Extremes Property of Proportions For any numbers a, b, c, and d, if " , then ad " bc.
Solve " .
" Original proportion
13(x) " 5(10) Cross products
13x " 50 Simplify.
" Divide each side by 13.
x " 3 Simplify.
The solution is 3 .
Solve each proportion.
1. " 2. " 3. "
4. " 5. " 6. "
7. " 8. " 9. "
10. " 11. " 12. "
13. " 14. " 15. "
Use a proportion to solve each problem.
16. MODELS To make a model of the Guadeloupe River bed, Hermie used 1 inch of clay for5 miles of the river’s actual length. His model river was 50 inches long. How long is theGuadeloupe River?
17. EDUCATION Josh finished 24 math problems in one hour. At that rate, how manyhours will it take him to complete 72 problems?
12%9
2 ' w%6
24%k
12%k
15%3
a # 8%12
#y%8
3 ' y%4
12%x
1.5%x
4%12
4%b # 2
p%24
5%8
18%3
3%d
18%54
9%y ' 1
3%63
x%21
8%x
4%6
3%4
x ' 1%4
0.5%x
0.1%2
5%3
1%t
2%8
#3%x
11%13
11%13
50%13
13x%13
10%13
x%5
10$13
x$5
c%d
a%b
10%13
x%5
Study Guide and Intervention (continued)
Ratios and Proportions
NAME ______________________________________________ DATE ____________ PERIOD _____
3-63-6
ExampleExample
ExercisesExercises
Skills PracticeRatios and Proportions
NAME ______________________________________________ DATE ____________ PERIOD _____
3-63-6
© Glencoe/McGraw-Hill 169 Glencoe Algebra 1
Less
on
3-6
Use cross products to determine whether each pair of ratios forms a proportion.Write yes or no.
1. , 2. ,
3. , 4. ,
5. , 6. ,
7. , 8. ,
Solve each proportion. If necessary, round to the nearest hundredth.
9. " 10. "
11. " 12. "
13. " 14. "
15. " 16. "
17. " 18. "
19. " 20. "
21. " 22. "
23. " 24. "
25. BOATING Hue’s boat used 5 gallons of gasoline in 4 hours. At this rate, how manygallons of gasoline will the boat use in 10 hours?
11%30
22%x
s%84
4%21
20%g
5%12
27%39
9%c
n%60
11%15
30%m
10%14
1%9
7%b
6%f
42%56
y%69
6%23
36%s
12%7
35%21
5%e
3%5
6%z
1%6
3%a
15%10
9%g
3%9
5%b
2%14
1%a
50%85
12%17
21%98
3%14
26%38
13%19
42%90
7%16
72%81
8%9
24%28
6%7
7%11
5%9
20%25
4%5
© Glencoe/McGraw-Hill 170 Glencoe Algebra 1
Use cross products to determine whether each pair of ratios forms a proportion.Write yes or no.
1. , 2. , 3. ,
4. , 5. , 6. ,
7. , 8. , 9. ,
Solve each proportion. If necessary, round to the nearest hundredth.
10. " 11. " 12. "
13. " 14. " 15. "
16. " 17. " 18. "
19. " 20. " 21. "
22. " 23. " 24. "
25. " 26. " 27. "
28. " 29. " 30. "
31. " 32. " 33. "
34. PAINTING Ysidra paints a room that has 400 square feet of wall space in 2 hours. At
this rate, how long will it take her to paint a room that has 720 square feet of wallspace?
35. VACATION PLANS Walker is planning a summer vacation. He wants to visit PetrifiedNational Forest and Meteor Crater, Arizona, the 50,000-year-old impact site of a largemeteor. On a map with a scale where 2 inches equals 75 miles, the two areas are about
1 inches apart. What is the distance between Petrified National Forest and Meteor
Crater?
1%2
1%2
x # 2%6
3%7
5%7
r ' 2%7
x ' 1%4
5%12
2%4
m # 1%8
2%y ' 6
3%12
14%6
7%a # 4
3%0.51
6%n
12%b
3%0.72
7%1.61
v%0.23
5%8
m%6
5%6
3%q
8%c
7%9
2%a
14%49
6%4
g%16
12%h
6%61
z%17
3%51
35%x
5%11
10%60
2%y
48%9
y%3
27%162
3%u
4%w
28%49
k%7
40%56
34%23
v%46
30%54
5%a
3.9%0.9
7.6%1.8
2.9%2.4
1.7%1.2
7.14%10.92
3.4%5.2
1%6
1.5%9
72%81
8%9
108%99
12%11
36%48
18%24
15%66
3%11
52%48
7%6
Practice Ratios and Proportions
NAME ______________________________________________ DATE ____________ PERIOD _____
3-63-6
Reading to Learn MathematicsRatios and Proportions
NAME ______________________________________________ DATE ____________ PERIOD _____
3-63-6
© Glencoe/McGraw-Hill 171 Glencoe Algebra 1
Less
on
3-6
Pre-Activity How are ratios used in recipes?
Read the introduction to Lesson 3-6 at the top of page 155 in your textbook.
• How many servings of honey frozen yogurt are made by this recipe?
• How many recipes would be needed to make enough honey frozen yogurtfor all the students in your class?
Reading the Lesson
1. Complete the following sentence.
A ratio is a comparison of two numbers by .
2. Describe two ways to decide whether the sentence " is a proportion.
3. For each proportion, tell what the extremes are and what the means are.
a. " Extremes: Means:
b. " Extremes: Means:
4. A jet flying at a steady speed traveled 825 miles in 2 hours. If you solved the proportion
" , what would the answer tell you about the jet?
Helping You Remember
5. Write how you would explain solving a proportion to a friend who missed Lesson 3-6.
x%1.5
825%2
12%16
6%8
6%15
14%35
8%20
2%5
© Glencoe/McGraw-Hill 172 Glencoe Algebra 1
Angles of a TriangleIn geometry, many statements about physical space are proven to betrue. Such statements are called theorems. Here are two examples ofgeometric theorems.
a. The sum of the measures of the angles of a triangle is 180°.b. If two sides of a triangle have equal measure, then the two angles
opposite those sides also have equal measure.
For each of the triangles, write an equation and then solve for x. (A tick mark ontwo or more sides of a triangle indicates that the sides have equal measure.)
1. 2.
3. 4.
5. 6.
7. 8.
9. 10.
11. Two angles of a triangle have the same 12. The measure of one angle of a triangle is measure. The sum of the measures of twice the measure of a second angle. The these angles is one-half the measure of measure of the third angle is 12 less than the third angle. Find the measures of the sum of the other two. Find the the angles of the triangle. measures of the angles of the triangle.
x2x
30°
x
40°
x
x # 15°
3x
x ' 30°
90°
4x
5x
5x
2x x
x ' 30°
x5x ' 10°
90° x
90° 45°
x70°
50°x
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
3-63-6
Study Guide and InterventionPercent of Change
NAME ______________________________________________ DATE ____________ PERIOD _____
3-73-7
© Glencoe/McGraw-Hill 173 Glencoe Algebra 1
Less
on
3-7
Percent of Change When an increase or decrease in an amount is expressed as apercent, the percent is called the percent of change. If the new number is greater than theoriginal number, the percent of change is a percent of increase. If the new number is lessthan the original number, the percent of change is the percent of decrease.
Find the percent of increase.original: 48new: 60
First, subtract to find the amount ofincrease. The amount of increase is 60 # 48 " 12.Then find the percent of increase by usingthe original number, 48, as the base.
" Percent proportion
12(100) " 48(r) Cross products
1200 " 48r Simplify.
" Divide each side by 48.
25 " r Simplify.
The percent of increase is 25%.
48r%48
1200%48
r%100
12%48
Find the percent of decrease.original: 30new: 22
First, subtract to find the amount ofdecrease. The amount of decrease is 30 # 22 " 8.Then find the percent of decrease by usingthe original number, 30, as the base.
" Percent proportion
8(100) " 30(r) Cross products
800 " 30r Simplify.
" Divide each side by 30.
26 " r Simplify.
The percent of decrease is 26 %, or about27%.
2%3
2%3
30r%30
800%30
r%100
8%30
Example 1Example 1 Example 2Example 2
ExercisesExercises
State whether each percent of change is a percent of increase or a percent ofdecrease. Then find each percent of change. Round to the nearest whole percent.
1. original: 50 2. original: 90 3. original: 45new: 80 new: 100 new: 20
4. original: 77.5 5. original: 140 6. original: 135new: 62 new: 150 new: 90
7. original: 120 8. original: 90 9. original: 27.5new: 180 new: 270 new: 25
10. original: 84 11. original: 12.5 12. original: 250new: 98 new: 10 new: 500
© Glencoe/McGraw-Hill 174 Glencoe Algebra 1
Solve Problems Discounted prices and prices including tax are applications of percentof change. Discount is the amount by which the regular price of an item is reduced. Thus,the discounted price is an example of percent of decrease. Sales tax is amount that is addedto the cost of an item, so the price including tax is an example of percent of increase.
A coat is on sale for 25% off the original price. If the original priceof the coat is $75, what is the discounted price?
The discount is 25% of the original price.
25% of $75 " 0.25 ! 75 25% " 0.25
" 18.75 Use a calculator.
Subtract $18.75 from the original price.$75 # $18.75 " $56.25
The discounted price of the coat is $56.25.
Find the final price of each item. When a discount and a sales tax are listed,compute the discount price before computing the tax.
1. Compact disc: $16 2. Two concert tickets: $28 3. Airline ticket: $248.00Discount: 15% Student discount: 28% Superair discount: 33%
4. Shirt: $24.00 5. CD player: $142.00 6. Celebrity calendar: $10.95Sales tax: 4% Sales tax: 5.5% Sales tax: 7.5%
7. Class ring: $89.00 8. Software: $44.00 9. Video recorder: $110.95Group discount: 17% Discount: 21% Discount: 20%Sales tax: 5% Sales tax: 6% Sales tax: 5%
10. VIDEOS The original selling price of a new sports video was $65.00. Due to the demandthe price was increased to $87.75. What was the percent of increase over the originalprice?
11. SCHOOL A high school paper increased its sales by 75% when it ran an issue featuringa contest to win a class party. Before the contest issue, 10% of the school’s 800 studentsbought the paper. How many students bought the contest issue?
12. BASEBALL Baseball tickets cost $15 for general admission or $20 for box seats. Thesales tax on each ticket is 8%, and the municipal tax on each ticket is an additional 10%of the base price. What is the final cost of each type of ticket?
Study Guide and Intervention (continued)
Percent of Change
NAME ______________________________________________ DATE ____________ PERIOD _____
3-73-7
ExampleExample
ExercisesExercises
Skills PracticePercent of Change
NAME ______________________________________________ DATE ____________ PERIOD _____
3-73-7
© Glencoe/McGraw-Hill 175 Glencoe Algebra 1
Less
on
3-7
State whether each percent of change is a percent of increase or a percent ofdecrease. Then find each percent of change. Round to the nearest whole percent.
1. original: 25 2. original: 50new: 10 new: 75
3. original: 55 4. original: 25new: 50 new: 28
5. original: 50 6. original: 90new: 30 new: 95
7. original: 48 8. original: 60new: 60 new: 45
Find the total price of each item.
9. dress: $69.00 10. binder: $14.50tax: 5% tax: 7%
11. hardcover book: $28.95 12. groceries: $47.52tax: 6% tax: 3%
13. filler paper: $6.00 14. shoes: $65.00tax: 6.5% tax: 4%
15. basketball: $17.00 16. concert tickets: $48.00tax: 6% tax: 7.5%
Find the discounted price of each item.
17. backpack: $56.25 18. monitor: $150.00discount: 20% discount: 50%
19. CD: $15.99 20. shirt: $25.50discount: 20% discount: 40%
21. sleeping bag: $125 22. coffee maker: $102.00discount: 25% discount: 45%
© Glencoe/McGraw-Hill 176 Glencoe Algebra 1
State whether each percent of change is a percent of increase or a percent ofdecrease. Then find each percent of change. Round to the nearest whole percent.
1. original: 18 2. original: 140 3. original: 200new: 10 new: 160 new: 320
4. original: 10 5. original: 76 6. original: 128new: 25 new: 60 new: 120
7. original: 15 8. original: 98.6 9. original: 58.8new: 35.5 new: 64 new: 65.7
Find the total price of each item.
10. concrete blocks: $95.00 11. crib: $240.00 12. jacket: $125.00tax: 6% tax: 6.5% tax: 5.5%
13. class ring: $325.00 14. blanket: $24.99 15. kite: $18.90tax: 6% tax: 7% tax: 5%
Find the discounted price of each item.
16. dry cleaning: $25.00 17. computer game: $49.99 18. luggage: $185.00discount: 15% discount: 25% discount: 30%
19. stationery: $12.95 20. prescription glasses: $149 21. pair of shorts: $24.99 discount: 10% discount: 20% discount: 45%
Find the final price of each item.
22. television: $375.00 23. DVD player: $269.00 24. printer: $255.00discount: 25% discount: 20% discount: 30%tax: 6% tax: 7% tax: 5.5%
25. INVESTMENTS The price per share of an internet-related stock decreased from $90 pershare to $36 per share early in 2001. By what percent did the price of the stockdecrease?
26. HEATING COSTS Customers of a utility company received notices in their monthly billsthat heating costs for the average customer had increased 125% over last year becauseof an unusually severe winter. In January of last year, the Garcia’s paid $120 for heating.What should they expect to pay this January if their bill increased by 125%?
Practice Percent of Change
NAME ______________________________________________ DATE ____________ PERIOD _____
3-73-7
Reading to Learn MathematicsPercent of Change
NAME ______________________________________________ DATE ____________ PERIOD _____
3-73-7
© Glencoe/McGraw-Hill 177 Glencoe Algebra 1
Less
on
3-7
Pre-Activity How can percents describe growth over time?
Read the introduction to Lesson 3-7 at the top of page 160 in your textbook.
• How many area codes were in use in 1947?
• How many more area codes were in use in 1999?
Reading the Lesson
1. If you use (original amount) — (new amount) to find the change for a percent of change problem, then the problem involves a percent of (increase/decrease).
2. If you use (new amount) — (original amount) to find the change for a percent of change problem, then the problem involves a percent of (increase/decrease).
Complete the chart.
Original New Percent Increase or Amount Amount
Percent ProportionPercent Decrease?
3. 10 13
4. 10 7
5. 50 42
6. 50 58
7. When you find a discount price, do you add to or subtract from the original price?
Helping You Remember
8. If you remember only two things about the ratio used for finding percent of change, whatshould they be?
© Glencoe/McGraw-Hill 178 Glencoe Algebra 1
Using PercentUse what you have learned about percent to solve each problem.
A TV movie had a “rating” of 15 and a 25 “share.” The rating is the percentageof the nation’s total TV households that were tuned in to this show. The shareis the percentage of homes with TVs turned on that were tuned to the movie.How many TV households had their TVs turned off at this time?To find out, let T ! the number of TV households
and x ! the number of TV households with the TV off.Then T " x ! the number of TV households with the TV on.
Since 0.15T and 0.25(T " x) both represent the number of households tunedto the movie,
0.15T ! 0.25(T " x)0.15T ! 0.25T " 0.25x.
Solve for x. 0.25x ! 0.10Tx ! ! 0.40T
Forty percent of the TV households had their TVs off when the movie was aired.
Answer each question.
1. During that same week, a sports broadcast had a rating of 22.1 and a 43 share.Show that the percent of TV households with their TVs off was about 48.6%.0.221T ! 0.43T " 0.43x
x !
! 0.486T2. Find the percent of TV households with their TVs turned off during a show
with a rating of 18.9 and a 29 share. 34.8%
3. Show that if T is the number of TV households, r is the rating, and s is the
share, then the number of TV households with the TV off is .Solve rT ! s(T " x) for x.
4. If the fraction of TV households with no TV on is then show that the
fraction of TV households with TVs on is .
5. Find the percent of TV households with TVs on during the most watched serial program in history: the last episode of M*A*S*H, which had a 60.3 rating and a 77 share. ! 78.3%
6. A local station now has a 2 share. Each share is worth $50,000 in advertising revenue per month. The station is thinking of going commercial free for the three months of summer to gain more listeners. What would its new share have to be for the last 4 months of the year to make more money for the year than it would have made had it not gone commercial free? greater than 3.5
60.3#77
r#s
s – r#s
(s " r)T#s
0.221T " 0.43T##
"0.43
0.10T#0.25
Enrichment
NAME ______________________________________________ DATE______________ PERIOD _____
3-73-7
1 " ! r#s
s " r#s
Study Guide and InterventionSolving Equations and Formulas
NAME ______________________________________________ DATE ____________ PERIOD _____
3-83-8
© Glencoe/McGraw-Hill 179 Glencoe Algebra 1
Less
on
3-8
Solve for Variables Sometimes you may want to solve an equation such as V " !wh forone of its variables. For example, if you know the values of V, w, and h, then the equation
! " is more useful for finding the value of !. If an equation that contains more than one
variable is to be solved for a specific variable, use the properties of equality to isolate thespecified variable on one side of the equation.
V%wh
Solve 2x ! 4y " 8 for y.
2x # 4y " 82x # 4y # 2x " 8 # 2x
#4y " 8 # 2x
"
y " or
The value of y is .2x # 8%4
2x # 8%4
8 # 2x%
#4
8 # 2x%
#4#4y%#4
Solve 3m ! n " km ! 8 for m.
3m # n " km # 83m # n # km " km # 8 # km3m # n # km " # 8
3m # n # km ' n " # 8 ' n3m # km " #8 ' nm(3 # k) " #8 ' n
"
m " , or
The value of m is . Since division by 0 is
undefined, 3 # k ( 0, or k ( 3.
n # 8%3 # k
n # 8%3 # k
#8 ' n%3 # k
#8 ' n%3 # k
m(3 # k)%%3 # k
Example 1Example 1 Example 2Example 2
ExercisesExercises
Solve each equation or formula for the variable specified.
1. ax # b " c for x 2. 15x ' 1 " y for x 3. (x ' f) ' 2 " j for x
4. xy ' z " 9 for y 5. x(4 # k) " p for k 6. 7x ' 3y " m for y
7. 4(c ' 3) " t for c 8. 2x ' b " c for x 9. x(1 ' y) " z for x
10. 16z ' 4x " y for x 11. d " rt for r 12. A " for h
13. C" (F # 32) for F 14. P " 2! ' 2w for w 15. A " !w for !5%9
h(a ' b)%%2
© Glencoe/McGraw-Hill 180 Glencoe Algebra 1
Use Formulas Many real-world problems require the use of formulas. Sometimes solvinga formula for a specified variable will help solve the problem.
The formula C " %d represents the circumference of a circle, or thedistance around the circle, where d is the diameter. If an airplane could fly aroundEarth at the equator without stopping, it would have traveled about 24,900 miles.Find the diameter of Earth.
C " &d Given formula
d " Solve for d.
d " Use & " 3.14.
d ! 7930 Simplify.
The diameter of Earth is about 7930 miles.
1. GEOMETRY The volume of a cylinder V is given by the formula V " &r2h, where r isthe radius and h is the height.
a. Solve the formula for h.
b. Find the height of a cylinder with volume 2500& feet and radius 10 feet.
2. WATER PRESSURE The water pressure on a submerged object is given by P " 64d,where P is the pressure in pounds per square foot, and d is the depth of the object in feet.
a. Solve the formula for d.
b. Find the depth of a submerged object if the pressure is 672 pounds per square foot.
3. GRAPHS The equation of a line containing the points (a, 0) and (0, b) is given by the
formula ' " 1.
a. Solve the equation for y.
b. Suppose the line contains the points (4, 0), and (0, #2). If x " 3, find y.
4. GEOMETRY The surface area of a rectangular solid is given by the formula S " 2!w ' 2!h ' 2wh, where ! " length, w " width, and h " height.
a. Solve the formula for h.
b. The surface area of a rectangular solid with length 6 centimeters and width 3 centimeters is 72 square centimeters. Find the height.
y%b
x%a
24,900%3.14
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Study Guide and Intervention (continued)
Solving Equations and Formulas
NAME ______________________________________________ DATE ____________ PERIOD _____
3-83-8
ExampleExample
ExercisesExercises
Skills PracticeSolving Equations and Formulas
NAME ______________________________________________ DATE ____________ PERIOD _____
3-83-8
© Glencoe/McGraw-Hill 181 Glencoe Algebra 1
Less
on
3-8
Solve each equation or formula for the variable specified.
1. 7t " x, for t 2. e " wp, for p
3. q # r " r, for r 4. 4m # n " m, for m
5. 7a # b " 15a, for a 6. #5c ' d " 2c, for c
7. x # 2y " 1, for y 8. m ' 3n " 1, for n
9. 7f ' g " 5, for f 10. ax # c " b, for x
11. rt # 2n " y, for t 12. bc ' 3g " 2k, for c
13. kn ' 4f " 9v, for n 14. 8c ' 6j " 5p, for c
15. " d, for x 16. " d, for c
17. " q, for p 18. " a, for b
Write an equation and solve for the variable specified.
19. Five more than a number g is six less than twice a number h. Solve for g.
20. One fourth of a number q is three more than three times a number w. Solve for q.
21. Eight less than a number s is three more than four times a number t. Solve for s.
b # 4z%7
p ' 9%5
x # c%2
x # c%2
© Glencoe/McGraw-Hill 182 Glencoe Algebra 1
Solve each equation or formula for the variable specified.
1. d " rt, for r 2. 6w # y " 2z, for w
3. mx ' 4y " 3c, for x 4. 9s # 5g " #4u, for s
5. ab ' 3c " 2d, for b 6. 2p " kx # q, for x
7. m ' a " a ' c, for m 8. h ' g " d, for h
9. y ' v " s, for y 10. a # q " k, for a
11. " h, for x 12. " c, for b
13. 2w # y " 7w # 2, for w 14. 3! ' y " 5 ' 5!, for !
Write an equation and solve for the variable specified.
15. Three times a number s plus 4 times a number y is 1 more than 6 times the number s.Solve for s.
16. Five times a number k minus 9 is two thirds of a number j. Solve for j.
ELECTRICITY For Exercises 17 and 18, use the following information.
The formula for Ohm’s Law is E " IR, where E represents voltage measured in volts,I represents current measured in amperes, and R represents resistance measured in ohms.
17. Solve the formula for R.
18. Suppose a current of 0.25 ampere flows through a resistor connected to a 12-volt battery.What is the resistance in the circuit?
MOTION For Exercises 19 and 20, use the following information.
In uniform circular motion, the speed v of a point on the edge of a spinning disk is v " r,
where r is the radius of the disk and T is the time it takes the point to travel once aroundthe circle.
19. Solve the formula for r.
20. Suppose a merry-go-round is spinning once every 3 seconds. If a point on the outsideedge has a speed of 12.56 feet per second, what is the radius of the merry-go-round? (Use 3.14 for &.)
2&%T
3b # 4%2
rx ' 9%5
3%4
2%3
2%5
2%3
Practice Solving Equations and Formulas
NAME ______________________________________________ DATE ____________ PERIOD _____
3-83-8
Reading to Learn MathematicsSolving Equations and Formulas
NAME ______________________________________________ DATE______________ PERIOD _____
3-83-8
© Glencoe/McGraw-Hill 183 Glencoe Algebra 1
Less
on 3
-8
Pre-Activity How are equations used to design roller coasters?
Read the introduction to Lesson 3-8 at the top of page 166 in your textbook.
The equation g(195 ! h) " v2 contains several variables. What
number values do you know for these variables in this situation?
32 for g and 49 for v
Reading the Lesson
1. Suppose you have an equation with several variables. You want to solve for a particularvariable. How does the procedure compare with that for solving an equation with justone variable? How does the solution compare with the solution for an equation with onevariable?
Sample answer: The procedure is basically the same. You use propertiesof operations and equality to isolate the variable in which you areinterested. The solution will probably contain variables instead of just anumber.
2. Describe what dimensional analysis involves.
Sample answer: You use the units along with number values as you docalculations. You treat the units pretty much the same way you wouldvariables. For example, you can divide them and use exponents with them.
3. What do you have to be careful about when you use variables in denominators offractions?
You have to be sure that you do not use values that would make thedenominator 0.
Helping You Remember
4. When you give the dimensions of a rectangle, you have to tell how many units long it isand how many units wide it is. How can this help you remember what dimensionalanalysis involves.
Sample answer: Keep the words dimension and unit in mind. Indimensional analysis, you include units for dimensions in calculations.
1#2
© Glencoe/McGraw-Hill 184 Glencoe Algebra 1
Dr. Bernardo Houssay Even though researchers have been studying the disease diabetesmellitus for hundreds of years, scientists have only recently discoveredthe cause of the disease and developed methods for reducing itsseverity. Dr. Bernardo Houssay, an Argentine physiologist, was one ofthe pioneers of this more modern research. He studied the relationshipbetween diabetes and the pituitary gland, and in 1947 became the firstLatin American to win the Nobel Prize in Medicine and Physiology.
Though there is no cure for diabetes, specific diets and exercise can helppeople control the disease. The American Diabetes Association (ADA)has helped establish flexible dietary guidelines for consumers to follow.These guidelines include some of the following general nutrition rules.
• Fat intake should be equal to or less than 30% of daily calories.
• Saturated fat intake should be equal to or less than 10% of dailycalories.
• Protein should be limited to 10% to 20% of daily calories. Personsshowing the initial signs of diabetes-induced kidney disease shouldlimit protein to 10% of daily calories.
• Cholesterol intake should be 300 milligrams or less daily.
Refer to the information above for Exercises 1–4.
1. Robert consumed 2100 calories on Tuesday. His fat intake totaled70 grams, and of that 70 grams, 14 were saturated.
a. What percentage of his calorie consumption was fat, and whatpercentage of that fat was saturated? (To find the percentage ofcalories from fat, multiply the number of fat grams by 9 beforedividing by the number of calories.) 30%; 20%
b. Did Robert stay within the recommended allowance of fats? yes
2. Anna's cholesterol intake was 330 milligrams on Sunday. By whatpercentage does she need to reduce her cholesterol consumption toremain within the guidelines? 10%
3. What number of fat grams is 30% of 240 calories? 8
4. Sharon follows a diet that provides about 50 grams of protein eachday. Sharon's doctor has just told her to reduce her daily proteinintake by 30%. About how much protein will be in her reducedprotein diet? 35 grams
Enrichment
NAME ______________________________________________ DATE______________ PERIOD _____
3-83-8
Study Guide and InterventionWeighted Averages
NAME ______________________________________________ DATE ____________ PERIOD _____
3-93-9
© Glencoe/McGraw-Hill 185 Glencoe Algebra 1
Less
on
3-9
Mixture Problems
Weighted AverageThe weighted average M of a set of data is the sum of the product of each number in the set and its weight divided by the sum of all the weights.
Mixture Problems are problems where two or more parts are combined into a whole. Theyinvolve weighted averages. In a mixture problem, the weight is usually a price or a percentof something.
Delectable Cookie Company sells chocolate chip cookies for $6.95per pound and white chocolate cookies for $5.95 per pound. How many pounds ofchocolate chip cookies should be mixed with 4 pounds of white chocolate cookiesto obtain a mixture that sells for $6.75 per pound.
Let w " the number of pounds of chocolate chip cookies
Number of Pounds Price per Pound Total Price
Chocolate Chip w 6.95 6.95w
White Chocolate 4 5.95 4(5.95)
Mixture w ' 4 6.75 6.75(w ' 4)
Equation: 6.95w ' 4(5.95) " 6.75(w ' 4)Solve the equation.
6.95w ' 4(5.95) " 6.75(w ' 4) Original equation6.95w ' 23.80 " 6.75w ' 27 Simplify.
6.95w ' 23.80 # 6.75w " 6.75w ' 27 # 6.75w Subtract 6.75w from each side.0.2w ' 23.80 " 27 Simplify.
0.2w ' 23.80 # 23.80 " 27 # 23.80 Subtract 23.80 from each side.0.2w " 3.2 Simplify.
w " 16 Simplify.
16 pounds of chocolate chip cookies should be mixed with 4 pounds of white chocolate cookies.
1. SOLUTIONS How many grams of sugar must be added to 60 grams of a solution that is32% sugar to obtain a solution that is 50% sugar?
2. NUTS The Quik Mart has two kinds of nuts. Pecans sell for $1.55 per pound andwalnuts sell for $1.95 per pound. How many pounds of walnuts must be added to 15pounds of pecans to make a mixture that sells for $1.75 per pound?
3. INVESTMENTS Alice Gleason invested a portion of $32,000 at 9% interest and thebalance at 11% interest. How much did she invest at each rate if her total income fromboth investments was $3,200.
4. MILK Whole milk is 4% butterfat. How much skim milk with 0% butterfat should beadded to 32 ounces of whole milk to obtain a mixture that is 2.5% butterfat?
ExampleExample
ExercisesExercises
© Glencoe/McGraw-Hill 186 Glencoe Algebra 1
Uniform Motion Problems Motion problems are another application of weightedaverages. Uniform motion problems are problems where an object moves at a certainspeed, or rate. Use the formula d " rt to solve these problems, where d is the distance, r isthe rate, and t is the time.
Bill Gutierrez drove at a speed of 65 miles per hour on anexpressway for 2 hours. He then drove for 1.5 hours at a speed of 45 miles perhour on a state highway. What was his average speed?
M " Definition of weighted average
! 56.4 Simplify.
Bill drove at an average speed of about 56.4 miles per hour.
1. TRAVEL Mr. Anders and Ms. Rich each drove home from a business meeting. Mr. Anderstraveled east at 100 kilometers per hour and Ms. Rich traveled west at 80 kilometers perhours. In how many hours were they 100 kilometers apart.
2. AIRPLANES An airplane flies 750 miles due west in 1 hours and 750 miles due south
in 2 hours. What is the average speed of the airplane?
3. TRACK Sprinter A runs 100 meters in 15 seconds, while sprinter B starts 1.5 secondslater and runs 100 meters in 14 seconds. If each of them runs at a constant rate, who isfurther in 10 seconds after the start of the race? Explain.
4. TRAINS An express train travels 90 kilometers per hour from Smallville to Megatown.A local train takes 2.5 hours longer to travel the same distance at 50 kilometers perhour. How far apart are Smallville and Megatown?
5. CYCLING Two cyclists begin traveling in the same direction on the same bike path. Onetravels at 15 miles per hour, and the other travels at 12 miles per hour. When will thecyclists be 10 miles apart?
6. TRAINS Two trains leave Chicago, one traveling east at 30 miles per hour and onetraveling west at 40 miles per hour. When will the trains be 210 miles apart?
1%2
65 ) 2 ' 45 ) 1.5%%2 ' 1.5
Study Guide and Intervention (continued)
Weighted Averages
NAME ______________________________________________ DATE ____________ PERIOD _____
3-93-9
ExampleExample
ExercisesExercises
Skills PracticeWeighted Averages
NAME ______________________________________________ DATE ____________ PERIOD _____
3-93-9
© Glencoe/McGraw-Hill 187 Glencoe Algebra 1
Less
on
3-9
SEASONING For Exercises 1–4, use the following information.
A health food store sells seasoning blends in bulk. One blend contains 20% basil. Sheilawants to add pure basil to some 20% blend to make 16 ounces of her own 30% blend. Let brepresent the amount of basil Sheila should add to the 20% blend.
1. Complete the table representing the problem.
Ounces Amount of Basil
20% Basil Blend
100% Basil
30% Basil Blend
2. Write an equation to represent the problem.
3. How many ounces of basil should Sheila use to make the 30% blend?
4. How many ounces of the 20% blend should she use?
HIKING For Exercises 5–7, use the following information.
At 7:00 A.M., two groups of hikers begin 21 miles apart and head toward each other. The firstgroup, hiking at an average rate of 1.5 miles per hour, carries tents, sleeping bags, andcooking equipment. The second group, hiking at an average rate of 2 miles per hour, carriesfood and water. Let t represent the hiking time.
5. Copy and complete the table representing the problem.
r t d " rt
First group of hikers
Second group of hikers
6. Write an equation using t that describes the distances traveled.
7. How long will it be until the two groups of hikers meet?
SALES For Exercises 8 and 9, use the following information.
Sergio sells a mixture of Virginia peanuts and Spanish peanuts for $3.40 per pound. Tomake the mixture, he uses Virginia peanuts that cost $3.50 per pound and Spanish peanutsthat cost $3.00 per pound. He mixes 10 pounds at a time.
8. How many pounds of Virginia peanuts does Sergio use?
9. How many pounds of Spanish peanuts does Sergio use?
© Glencoe/McGraw-Hill 188 Glencoe Algebra 1
GRASS SEED For Exercises 1–4, use the following information.
A nursery sells Kentucky Blue Grass seed for $5.75 per pound and Tall Fescue seed for$4.50 per pound. The nursery sells a mixture of the two kinds of seed for $5.25 per pound.Let k represent the amount of Kentucky Blue Grass seed the nursery uses in 5 pounds ofthe mixture.
1. Complete the table representing the problem.
Number of Pounds Price per Pound Cost
Kentucky Blue Grass
Tall Fescue
Mixture
2. Write an equation to represent the problem.
3. How much Kentucky Blue Grass does the nursery use in 5 pounds of the mixture?
4. How much Tall Fescue does the nursery use in 5 pounds of the mixture?
TRAVEL For Exercises 5–7, use the following information.
Two commuter trains carry passengers between two cities, one traveling east, and the otherwest, on different tracks. Their respective stations are 150 miles apart. Both trains leave atthe same time, one traveling at an average speed of 55 miles per hour and the other at anaverage speed of 65 miles per hour. Let t represent the time until the trains pass each other.
5. Copy and complete the table representing the problem.
r t d " rt
First Train
Second Train
6. Write an equation using t that describes the distances traveled.
7. How long after departing will the trains pass each other?
8. TRAVEL Two trains leave Raleigh at the same time, one traveling north, and the othersouth. The first train travels at 50 miles per hour and the second at 60 miles per hour.In how many hours will the trains be 275 miles apart?
9. JUICE A pineapple drink contains 15% pineapple juice. How much pure pineapple juiceshould be added to 8 quarts of the drink to obtain a mixture containing 50% pineapplejuice?
Practice Weighted Averages
NAME ______________________________________________ DATE ____________ PERIOD _____
3-93-9
Reading to Learn MathematicsWeighted Averages
NAME ______________________________________________ DATE ____________ PERIOD _____
3-93-9
© Glencoe/McGraw-Hill 189 Glencoe Algebra 1
Less
on
3-9
Pre-Activity How are scores calculated in a figure skating competition?
Read the introduction to Lesson 3-9 at the top of page 171 in your textbook.
Why is the sum of Ilia Kulik’s scores divided by 3?
Reading the Lesson
1. Read the definition of weighted average on page 171 of your textbook. What is meant bythe weight of a number in a set of data?
2. Linda’s quiz scores in science are 90, 85, 85, 75, 85, and 90. What is the weight of thescore 85?
3. Suppose Clint drives at 50 miles per hour for 2 hours. Then he drives at 60 miles perhour for 3 hours.
a. Write his speed for each hour of the trip.
Speed
Hour 1 2 3 4 5
b. What is the weight of each of the two speeds?
Helping You Remember
4. Making a table can be helpful in solving mixture problems. In your own words, explainhow you use a table to solve mixture problems.
© Glencoe/McGraw-Hill 190 Glencoe Algebra 1
Diophantine EquationsThe first great algebraist, Diophantus of Alexandria (about A.D. 300),devoted much of his work to the solving of indeterminate equations.An indeterminate equation has more than one variable and anunlimited number of solutions. An example is x ' 2y " 4.
When the coefficients of an indeterminate equation are integers andyou are asked to find solutions that must be integers, the equation iscalled diophantine. Such equations can be quite difficult to solve,often involving trial and error—and some luck!
Solve each diophantine equation by finding at least one pair of positive integers that makes the equation true. Some hints are given to help you.
1. 2x ' 5y " 32
a. First solve the equation for x.
b. Why must y be an even number?
c. Find at least one solution.
2. 5x ' 2y " 42
a. First solve the equation for x.
b. Rewrite your answer in the form x " 8 ' some expression.
c. Why must (2 # 2y) be a multiple of 5?
d. Find at least one solution.
3. 2x ' 7y " 29 4. 7x ' 5y " 118
5. 8x # 13y " 100 6. 3x ' 4y " 22
7. 5x # 14y " 11 8. 7x ' 3y " 40
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
3-93-9
© Glencoe/McGraw-Hill A2 Glencoe Algebra 1
Stu
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Gu
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ce o
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is e
qual
to
9.F
and
32.
11.V
"B
h12
.A
"hb
Vis
equ
al t
o of
the
pro
duct
of
Ais
equ
al t
o of
the
pro
duct
of
Ban
d h.
han
d b.
1 % 21 % 3
1 % 21 % 3
5 % 9
5 % 91 % 31 % 3
Stu
dy
Gu
ide
and I
nte
rven
tion
(c
onti
nued
)
Wri
ting
Equ
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-1
3-1
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 3-1)
© Glencoe/McGraw-Hill A3 Glencoe Algebra 1
An
swer
s
Skil
ls P
ract
ice
Wri
ting
Equ
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-1
3-1
©G
lenc
oe/M
cGra
w-H
ill13
9G
lenc
oe A
lgeb
ra 1
Lesson 3-1
Tra
nsl
ate
each
sen
ten
ce i
nto
an
equ
atio
n.
1.T
wo
adde
d to
thr
ee t
imes
a n
umbe
r m
is t
he s
ame
as 1
8.3m
#2
"18
2.T
wic
e a
incr
ease
d by
the
cub
e of
aeq
uals
b.
2a#
a3"
b
3.Se
ven
less
tha
n th
e su
m o
f pan
d q
is a
s m
uch
as 6
.(p
#q
) !
7 "
6
4.T
he s
um o
f xan
d it
s sq
uare
is e
qual
to
yti
mes
z.
x #
x2
"yz
5.Fo
ur t
imes
the
sum
of f
and
gis
iden
tica
l to
six
tim
es g
.4(
f#
g)
"6g
Tra
nsl
ate
each
sen
ten
ce i
nto
a f
orm
ula
.
6.T
he p
erim
eter
Pof
a s
quar
e eq
uals
fou
r ti
mes
the
leng
th o
f a
side
s.
P"
4s
7.T
he a
rea
Aof
a s
quar
e is
the
leng
th o
f a
side
ssq
uare
d.A
"s2
8.T
he p
erim
eter
Pof
a t
rian
gle
is e
qual
to
the
sum
of
the
leng
ths
of s
ides
a,b
,and
c.
P"
a#
b#
c9.
The
are
a A
of a
cir
cle
is p
i tim
es t
he r
adiu
s r
squa
red.
A"
$r2
10.T
he v
olum
e V
of a
rec
tang
ular
pri
sm e
qual
s th
e pr
oduc
t of
the
leng
th !
,the
wid
th w
,an
d th
e he
ight
h.
V"
!wh
Tra
nsl
ate
each
equ
atio
n i
nto
a v
erba
l se
nte
nce
.
11.g
'10
"3g
12.2
p'
4q"
20g
plus
10
is t
he s
ame
asTw
ice
ppl
us 4
tim
es q
is 2
0.3
times
g.
13.4
(a'
b) "
9a14
.8 #
6x"
4 '
2x4
times
the
sum
of
aan
d b
8 m
inus
6 t
imes
xis
4 p
lus
is
9 t
imes
a.
2 tim
es x
.
15.
(f'
y) "
f#
516
.s2
#n2
"2b
Hal
f of
the
sum
of
fan
d y
is
ssq
uare
d m
inus
nsq
uare
d is
f
min
us 5
.tw
ice
b.
Wri
te a
pro
blem
bas
ed o
n t
he
give
n i
nfo
rmat
ion
.
17.c
"co
st p
er p
ound
of
plai
n co
ffee
bea
ns18
.p"
cost
of
dinn
erc
'3
"co
st p
er p
ound
of
flav
ored
cof
fee
bean
s0.
15p
"co
st o
f a
15%
tip
2c'
(c'
3) "
21p
'0.
15p
"23
Sam
ple
answ
er:T
he c
ost
of t
wo
poun
ds
Sam
ple
answ
er:T
he c
ost
ofof
pla
in c
offe
e be
ans
plus
one
pou
nd o
fdi
nner
plu
s a
15%
tip
was
fla
vore
d be
ans
is $
21.H
ow m
uch
does
$2
3.H
ow m
uch
was
the
1
poun
d of
pla
in b
eans
cos
t?di
nner
?
1 % 2
©G
lenc
oe/M
cGra
w-H
ill14
0G
lenc
oe A
lgeb
ra 1
Tra
nsl
ate
each
sen
ten
ce i
nto
an
equ
atio
n.
1.F
ifty
-thr
ee p
lus
four
tim
es c
is a
s m
uch
as 2
1.53
#4c
"21
2.T
he s
um o
f fi
ve t
imes
han
d tw
ice
gis
equ
al t
o 23
.5h
#2g
"23
3.O
ne f
ourt
h th
e su
m o
f ran
d te
n is
iden
tica
l to
rm
inus
4.
(r#
10)
"r
!4
4.T
hree
plu
s th
e su
m o
f th
e sq
uare
s of
wan
d x
is 3
2.3
#(w
2#
x2 )
"32
Tra
nsl
ate
each
sen
ten
ce i
nto
a f
orm
ula
.
5.D
egre
es K
elvi
n K
equa
ls 2
73 p
lus
degr
ees
Cel
sius
C.
K"
273
#C
6.T
he t
otal
cos
t C
of g
as is
the
pri
ce p
per
gallo
n ti
mes
the
num
ber
of g
allo
ns g
.C
"pg
7.T
he s
um S
of
the
mea
sure
s of
the
ang
les
of a
pol
ygon
is e
qual
to
180
tim
es t
he d
iffe
renc
eof
the
num
ber
of s
ides
nan
d 2.
S"
180(
n!
2)
Tra
nsl
ate
each
equ
atio
n i
nto
a v
erba
l se
nte
nce
.
8.q
#(4
'p)
"q
qm
inus
the
sum
9.
t'
2 "
t
of 4
and
p e
qual
s tim
es q
.Tw
o m
ore
than
of
teq
uals
t.
10.9
(y2
'x)
"18
9 tim
es t
he s
um
11.2
(m#
n) "
v'
7Tw
ice
the
quan
tity
of y
squa
red
and
xis
18.
mm
inus
nis
vpl
us 7
.
Wri
te a
pro
blem
bas
ed o
n t
he
give
n i
nfo
rmat
ion
.
12.a
"co
st o
f on
e ad
ult’s
tic
ket
to z
oo13
.c"
regu
lar
cost
of
one
airl
ine
tick
eta
#4
"co
st o
f one
chi
ldre
n’s
tick
et t
o zo
o0.
20c
"am
ount
of 2
0% p
rom
otio
nal d
isco
unt
2a'
4(a
#4)
"38
3(c
#0.
20c)
"33
0S
ampl
e an
swer
:The
cos
t of
tw
o S
ampl
e an
swer
:The
cos
t of
thr
ee
adul
t’s t
icke
ts a
nd 4
chi
ldre
n’s
airl
ine
ticke
ts t
hat
are
disc
ount
ed
ticke
ts t
o th
e zo
o is
$38
.How
20
% is
$33
0.W
hat
is t
he r
egul
ar
muc
h is
an
adul
t’s t
icke
t?co
st o
f a
ticke
t?
14.G
EOG
RA
PHY
Abo
ut 1
5% o
f al
l fed
eral
ly-o
wne
d la
nd in
the
48
cont
iguo
us s
tate
s of
the
Uni
ted
Stat
es is
in N
evad
a.If
Fre
pres
ents
the
are
a of
fed
eral
ly-o
wne
d la
nd in
the
sest
ates
,and
Nre
pres
ents
the
por
tion
in N
evad
a,w
rite
an
equa
tion
for
thi
s si
tuat
ion.
0.15
F"
N
FITN
ESS
For
Exe
rcis
es 1
5–17
,use
th
e fo
llow
ing
info
rmat
ion
.D
eann
a an
d P
ietr
a ea
ch g
o fo
r w
alks
aro
und
a la
ke a
few
tim
es p
er w
eek.
Las
t w
eek,
Dea
nna
wal
ked
7 m
iles
mor
e th
an P
ietr
a.15
.If
pre
pres
ents
the
num
ber
of m
iles
Pie
tra
wal
ked,
wri
te a
n eq
uati
on t
hat
repr
esen
ts t
heto
tal n
umbe
r of
mile
s T
the
two
girl
s w
alke
d.T
"p
#(p
#7)
16.I
f P
ietr
a w
alke
d 9
mile
s du
ring
the
wee
k,ho
w m
any
mile
s di
d D
eann
a w
alk?
16 m
i17
.If
Pie
tra
wal
ked
11 m
iles
duri
ng t
he w
eek,
how
man
y m
iles
did
the
two
girl
s w
alk
toge
ther
?29
mi
3 % 51 % 3
3 % 51 % 3
1 % 4
Pra
ctic
e (A
vera
ge)
Wri
ting
Equ
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-1
3-1
Answers (Lesson 3-1)
© Glencoe/McGraw-Hill A4 Glencoe Algebra 1
Rea
din
g t
o L
earn
Math
emati
csW
ritin
g E
quat
ions
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-1
3-1
©G
lenc
oe/M
cGra
w-H
ill14
1G
lenc
oe A
lgeb
ra 1
Lesson 3-1
Pre-
Act
ivit
yH
ow a
re e
quat
ion
s u
sed
to
des
crib
e h
eigh
ts?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 3-
1 at
the
top
of
page
120
in y
our
text
book
.
Doe
s th
e eq
uati
on 3
05 #
s"
154
also
rep
rese
nt t
he s
itua
tion
?E
xpla
in.
Yes;
the
tota
l hei
ght
min
us t
he h
eigh
t of
the
sta
tue
itsel
f gi
ves
the
heig
ht o
f th
e pe
dest
al.
Rea
din
g t
he
Less
on
1.T
rans
late
eac
h se
nten
ce in
to a
n eq
uati
on.
a.Tw
otim
esth
e su
m o
f xan
d th
ree
min
usfo
ureq
uals
four
times
x.
2&
(x#
3)!
4"
4&
x
b.T
he d
iffer
ence
of k
and
3is
two
times
kdi
vide
d by
five.
k!
3"
2&
k'
5
2.A
1 o
z se
rvin
g of
chi
ps h
as 1
40 c
alor
ies.
The
re a
re a
bout
14
serv
ings
of
chip
s in
a b
ag.
How
man
y ca
lori
es a
re t
here
in a
bag
of
chip
s? W
rite
wha
t yo
ur s
olut
ion
wou
ld b
e as
you
use
each
ste
p in
the
Fou
r-St
ep P
robl
em-S
olvi
ng P
lan.
Exp
lore
Wha
t do
you
kno
w?
A 1
oz
serv
ing
of c
hips
has
140
cal
orie
s an
d th
ere
are
14se
rvin
gs o
f ch
ips
in a
bag
.W
hat
do y
ou w
ant
to k
now
?
How
man
y ca
lori
es a
re in
a b
ag o
f ch
ips?
Pla
nW
rite
an
equa
tion
.
140
(14
"x
Sol
veSo
lve
the
prob
lem
.
140
(14
"19
60;T
here
are
196
0 ca
lori
es in
a b
ag o
f ch
ips.
Exa
min
eD
oes
your
ans
wer
mak
e se
nse?
See
stu
dent
s’w
ork.
Hel
pin
g Y
ou
Rem
emb
er
3.If
you
can
not
rem
embe
r al
l the
ste
ps o
f th
e Fo
ur-S
tep
Pro
blem
-Sol
ving
Pla
n,tr
y to
rem
embe
r th
e fi
rst
lett
ers
of t
he f
irst
wor
d in
eac
h st
ep.W
rite
tho
se le
tter
s he
re w
ith
thei
r as
soci
ated
wor
ds.
EP
SE
;Exp
lore
,Pla
n,S
olve
,Exa
min
e
©G
lenc
oe/M
cGra
w-H
ill14
2G
lenc
oe A
lgeb
ra 1
Rep
-Tile
sA
rep
-tile
is a
fig
ure
that
can
be
subd
ivid
ed in
to
smal
ler
copi
es o
f it
self.
The
larg
e fi
gure
is s
imila
r to
the
sm
all o
nes
and
the
smal
l fig
ures
are
all
cong
ruen
t.
Sh
ow t
hat
eac
h f
igu
re i
s a
rep
-til
e by
su
bdiv
idin
g it
in
to f
our
smal
ler
and
si
mil
ar f
igu
res.
1.2.
3.
4.5.
6.
Su
bdiv
ide
each
rep
-til
e in
to n
ine
smal
ler
and
sim
ilar
fig
ure
s.
7.8.
9.10
.
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-1
3-1
Answers (Lesson 3-1)
© Glencoe/McGraw-Hill A5 Glencoe Algebra 1
An
swer
s
Stu
dy
Gu
ide
an
d I
nte
rven
tion
Sol
ving
Equ
atio
ns b
y U
sing
Add
ition
and
Sub
trac
tion
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-2
3-2
©G
lenc
oe/M
cGra
w-H
ill14
3G
lenc
oe A
lgeb
ra 1
Lesson 3-2
Solv
e U
sin
g A
dd
itio
nIf
the
sam
e nu
mbe
r is
add
ed t
o ea
ch s
ide
of a
n eq
uati
on,t
here
sult
ing
equa
tion
is e
quiv
alen
t to
the
ori
gina
l one
.In
gene
ral i
f th
e or
igin
al e
quat
ion
invo
lves
sub
trac
tion
,thi
s pr
oper
ty w
ill h
elp
you
solv
e th
e eq
uati
on.
Add
ition
Pro
pert
y of
Equ
ality
For
any
num
bers
a, b
, and
c, i
f a"
b, th
en a
'c
"b
'c.
Sol
ve m
!32
"18
.
m#
32 "
18O
rigin
al e
quat
ion
m#
32 '
32 "
18 '
32A
dd 3
2 to
eac
h si
de.
m"
50S
impl
ify.
The
sol
utio
n is
50.
Sol
ve !
18 "
p!
12.
#18
"p
#12
Orig
inal
equ
atio
n
#18
'12
"p
#12
'12
Add
12
to e
ach
side
.
p"
#6
Sim
plify
.
The
sol
utio
n is
#6.
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Sol
ve e
ach
equ
atio
n.T
hen
ch
eck
you
r so
luti
on.
1.h
#3
"#
21
2.m
#8
"#
12!
43.
p#
5 "
1520
4.20
"y
#8
285.
k#
0.5
"2.
32.
86.
w#
"1
7.h
#18
"#
171
8.#
12 "
#24
'k
129.
j#0.
2 "
1.8
2
10.b
#40
"#
400
11.m
#(#
12)
"10
!2
12.w
#"
Wri
te a
n e
quat
ion
for
eac
h p
robl
em.T
hen
sol
ve t
he
equ
atio
n a
nd
ch
eck
th
eso
luti
on.
13.T
wel
ve s
ubtr
acte
d fr
om a
num
ber
equa
ls 2
5.F
ind
the
num
ber.
n!
12 "
25;3
7
14.W
hat
num
ber
decr
ease
d by
52
equa
ls #
12?
n!
52 "
!12
;40
15.F
ifty
sub
trac
ted
from
a n
umbe
r eq
uals
eig
hty.
Fin
d th
e nu
mbe
r.n
!50
"80
;130
16.W
hat
num
ber
min
us o
ne-h
alf
is e
qual
to
nega
tive
one
-hal
f?n
!
"!
;0
17.T
he d
iffe
renc
e of
a n
umbe
r an
d ei
ght
is e
qual
to
14.W
hat
is t
he n
umbe
r?
n!
8 "
14;2
2
18.A
num
ber
decr
ease
d by
fou
rtee
n is
equ
al t
o ei
ghte
en.W
hat
is t
he n
umbe
r?n
!14
"18
;32
1 % 21 % 2
7 % 41 % 4
3 % 2
1 % 85 % 8
1 % 2
©G
lenc
oe/M
cGra
w-H
ill14
4G
lenc
oe A
lgeb
ra 1
Solv
e U
sin
g S
ub
trac
tio
nIf
the
sam
e nu
mbe
r is
sub
trac
ted
from
eac
h si
de o
f an
equa
tion
,the
res
ulti
ng e
quat
ion
is e
quiv
alen
t to
the
ori
gina
l one
.In
gene
ral i
f th
e or
igin
aleq
uati
on in
volv
es a
ddit
ion,
this
pro
pert
y w
ill h
elp
you
solv
e th
e eq
uati
on.
Sub
trac
tion
Pro
pert
y of
Equ
ality
For
any
num
bers
a, b
, and
c, i
f a "
b, th
en a
#c
"b
#c.
Sol
ve 2
2 #
p"
!12
.
22 '
p"
#12
Orig
inal
equ
atio
n
22 '
p#
22 "
#12
#22
Sub
trac
t 22
from
eac
h si
de.
p"
#34
Sim
plify
.
The
sol
utio
n is
#34
.
Sol
ve e
ach
equ
atio
n.T
hen
ch
eck
you
r so
luti
on.
1.x
'12
"6
!6
2.z
'2
"#
13!
153.
#17
"b
'4
!21
4.s
'(#
9) "
716
5.#
3.2
"!
'(#
0.2)
!3
6.#
'x
"1
7.19
'h
"#
4!
238.
#12
"k
'24
!36
9.j'
1.2
"2.
81.
6
10.b
'80
"#
80!
160
11.m
'(#
8) "
210
12.w
'"
!
Wri
te a
n e
quat
ion
for
eac
h p
robl
em.T
hen
sol
ve t
he
equ
atio
n a
nd
ch
eck
th
eso
luti
on.
13.T
wel
ve a
dded
to
a nu
mbe
r eq
uals
18.
Fin
d th
e nu
mbe
r.n
#12
"18
;6
14.W
hat
num
ber
incr
ease
d by
20
equa
ls #
10?
n#
20 "
!10
;!30
15.T
he s
um o
f a
num
ber
and
fift
y eq
uals
eig
hty.
Fin
d th
e nu
mbe
r.n
#50
"80
;30
16.W
hat
num
ber
plus
one
-hal
f is
equ
al t
o fo
ur?
n#
"4;
3
17.T
he s
um o
f a
num
ber
and
3 is
equ
al t
o #
15.W
hat
is t
he n
umbe
r?n
#3
"!
15;!
18
1 % 21 % 2
7 % 85 % 8
3 % 2
5 % 83 % 8
Stu
dy
Gu
ide
and I
nte
rven
tion
(c
onti
nued
)
Sol
ving
Equ
atio
ns b
y U
sing
Add
ition
and
Sub
trac
tion
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-2
3-2
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 3-2)
© Glencoe/McGraw-Hill A6 Glencoe Algebra 1
Skil
ls P
ract
ice
Sol
ving
Equ
atio
ns b
y U
sing
Add
ition
and
Sub
trac
tion
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-2
3-2
©G
lenc
oe/M
cGra
w-H
ill14
5G
lenc
oe A
lgeb
ra 1
Lesson 3-2
Sol
ve e
ach
equ
atio
n.T
hen
ch
eck
you
r so
luti
on.
1.y
#7
"8
152.
w'
14 "
#8
!22
3.p
#4
"6
104.
#13
"5
'x
!18
5.98
"b
'34
646.
y#
32 "
#1
31
7.s
'(#
28)
"0
288.
y'
(#10
) "
616
9.#
1 "
s'
(#19
)18
10.j
#(#
17)
"36
19
11.1
4 "
d'
(#10
)24
12.u
'(#
5) "
#15
!10
13.1
1 "
#16
'y
2714
.c#
(#3)
"10
097
15.4
7 "
w#
(#8)
3916
.x#
(#74
) "
#22
!96
17.4
#(#
h) "
6864
18.#
56 "
20 #
(#e)
!76
Wri
te a
n e
quat
ion
for
eac
h p
robl
em.T
hen
sol
ve t
he
equ
atio
n a
nd
ch
eck
you
rso
luti
on.
19.A
num
ber
decr
ease
d by
14
is #
46.F
ind
the
num
ber.
n!
14 "
!46
;!32
20.T
hirt
een
subt
ract
ed f
rom
a n
umbe
r is
#5.
Fin
d th
e nu
mbe
r.n
!13
"!
5;8
21.T
he s
um o
f a
num
ber
and
67 is
equ
al t
o #
34.F
ind
the
num
ber.
n#
67 "
!34
;!10
1
22.W
hat
num
ber
min
us 2
8 eq
uals
#2?
n!
28 "
!2;
26
23.A
num
ber
plus
#73
is e
qual
to
27.W
hat
is t
he n
umbe
r?n
#(!
73)
"27
;100
24.A
num
ber
plus
#17
equ
als
#1.
Fin
d th
e nu
mbe
r.n
#(!
17)
"!
1;16
25.W
hat
num
ber
less
5 is
equ
al t
o #
39?
n!
5 "
!39
;!34
©G
lenc
oe/M
cGra
w-H
ill14
6G
lenc
oe A
lgeb
ra 1
Sol
ve e
ach
equ
atio
n.T
hen
ch
eck
you
r so
luti
on.
1.d
#8
"17
252.
v'
12 "
#5
!17
3.b
#2
"#
11!
9
4.#
16 "
s'
71!
875.
29 "
a#
7610
56.
#14
'y
"#
212
7.8
#(#
c) "
1!
78.
78 '
r"
#15
!93
9.f
'(#
3) "
#9
!6
10.4
.2 "
n'
7.3
!3.
111
.w'
1.9
"#
2.5
!4.
412
.4.6
#(#
b) "
#0.
4!
5
13.y
#(#
1.5)
"0.
5!
114
.a#
0.13
"#
0.58
!0.
4515
.k'
(#4.
21)
"#
19!14
.79
16.r
'"
17.
'q
"18
."
h'
!
19.
'x
"#
!20
.y'
"!
21.#
#(#
n) "
#
Wri
te a
n e
quat
ion
for
eac
h p
robl
em.T
hen
sol
ve t
he
equ
atio
n a
nd
ch
eck
you
rso
luti
on.
22.W
hat
num
ber
min
us 9
is e
qual
to
#18
?n
!9
"!
18;!
9
23.A
num
ber
plus
15
equa
ls #
12.W
hat
is t
he n
umbe
r?n
#15
"!
12;!
27
24.T
he s
um o
f a
num
ber
and
#3
is e
qual
to
#91
.Fin
d th
e nu
mbe
r.n
#(!
3) "
!91
;!88
25.N
egat
ive
seve
ntee
n eq
uals
63
plus
a n
umbe
r.W
hat
is t
he n
umbe
r?!
17 "
63 #
n;!
8026
.The
sum
of
nega
tive
14,
a nu
mbe
r,an
d 6
is #
5.W
hat
is t
he n
umbe
r?!
14 #
n#
6 "
!5;
327
.Wha
t nu
mbe
r pl
us o
ne h
alf
is e
qual
to
thre
e ei
ghth
s?n
#"
;!
HIS
TORY
For
Exe
rcis
es 2
8 an
d 2
9,u
se t
he
foll
owin
g in
form
atio
n.
Gal
ileo
Gal
ilei w
as b
orn
in 1
564.
Man
y ye
ars
late
r,in
164
2,Si
r Is
aac
New
ton
was
bor
n.
28.W
rite
an
addi
tion
equ
atio
n to
rep
rese
nt t
he s
itua
tion
.15
64 #
y"
1642
29.H
ow m
any
year
s af
ter
Gal
ileo
was
bor
n w
as I
saac
New
ton
born
?78
HU
RR
ICA
NES
For
Exe
rcis
es 3
0 an
d 3
1,u
se t
he
foll
owin
g in
form
atio
n.
The
day
aft
er a
hur
rica
ne,t
he b
arom
etri
c pr
essu
re in
a c
oast
al t
own
has
rise
n to
29
.7 in
ches
of
mer
cury
,whi
ch is
2.9
inch
es o
f m
ercu
ry h
ighe
r th
an t
he p
ress
ure
whe
n th
eey
e of
the
hur
rica
ne p
asse
d ov
er.
30.W
rite
an
addi
tion
equ
atio
n to
rep
rese
nt t
he s
itua
tion
.b
#2.
9 "
29.7
31.W
hat
was
the
bar
omet
ric
pres
sure
whe
n th
e ey
e pa
ssed
ove
r?26
.8 in
.of
mer
cury
1 % 83 % 8
1 % 2
7 % 247 % 12
7 % 81 % 20
3 % 44 % 5
5 % 67 % 12
1 % 4
1 % 152 % 5
1 % 31 % 9
2 % 35 % 9
7 % 109 % 10
1 % 5
Pra
ctic
e (A
vera
ge)
Sol
ving
Equ
atio
ns b
y U
sing
Add
ition
and
Sub
trac
tion
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-2
3-2
Answers (Lesson 3-2)
© Glencoe/McGraw-Hill A7 Glencoe Algebra 1
An
swer
s
Rea
din
g t
o L
earn
Math
emati
csS
olvi
ng E
quat
ions
by
Usi
ng A
dditi
on a
nd S
ubtr
actio
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-2
3-2
©G
lenc
oe/M
cGra
w-H
ill14
7G
lenc
oe A
lgeb
ra 1
Lesson 3-2
Pre-
Act
ivit
yH
ow c
an e
quat
ion
s be
use
d t
o co
mp
are
dat
a?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 3-
2 at
the
top
of
page
128
in y
our
text
book
.
In t
he e
quat
ion
m#
66 "
5,th
e nu
mbe
r 5
repr
esen
ts
the
diff
eren
ce b
etw
een
the
perc
ent
of g
row
th fo
r m
edic
al
assi
stan
ts a
nd t
he p
erce
nt o
f gr
owth
for
trav
el a
gent
s,an
d th
e nu
mbe
r 66
rep
rese
nts
the
rate
of
grow
th fo
r tr
avel
age
nts.
Rea
din
g t
he
Less
on
1.To
sol
ve x
'17
"46
usi
ng t
he S
ubtr
acti
on P
rope
rty
of E
qual
ity,
you
wou
ld s
ubtr
act
from
eac
h si
de.
2.To
sol
ve y
#9
"#
30 u
sing
the
Add
itio
n P
rope
rty
of E
qual
ity,
you
wou
ld a
dd
to e
ach
side
.
3.W
rite
an
equa
tion
tha
t yo
u co
uld
solv
e by
sub
trac
ting
32
from
eac
h si
de.
Sam
ple
answ
er:m
#32
"50
4.A
stu
dent
use
d th
e Su
btra
ctio
n P
rope
rty
of E
qual
ity
to s
olve
an
equa
tion
.Exp
lain
why
itw
ould
als
o be
pos
sibl
e to
use
the
Add
itio
n P
rope
rty
of E
qual
ity
to s
olve
the
equ
atio
n.S
ubtr
actin
g on
e nu
mbe
r fr
om a
noth
er g
ives
the
sam
e re
sult
as a
ddin
gth
e op
posi
te o
f th
e nu
mbe
r th
at w
as s
ubtr
acte
d.
Hel
pin
g Y
ou
Rem
emb
er
5.E
xpla
in h
ow y
ou d
ecid
e w
heth
er t
o us
e th
e A
ddit
ion
Pro
pert
y or
the
Sub
trac
tion
Pro
pert
y of
Equ
alit
y to
sol
ve a
n eq
uati
on.
Sam
ple
answ
er:I
f th
e gi
ven
equa
tion
has
a nu
mbe
r ad
ded
to t
heva
riab
le,t
hen
use
the
Sub
trac
tion
Pro
pert
y of
Equ
ality
.If
the
equa
tion
has
a nu
mbe
r su
btra
cted
fro
m t
he v
aria
ble,
then
use
the
Add
ition
Pro
pert
y of
Equ
ality
.
917
©G
lenc
oe/M
cGra
w-H
ill14
8G
lenc
oe A
lgeb
ra 1
Cou
ntin
g-O
ff P
uzzl
esS
olve
eac
h p
uzz
le.
1.T
wen
ty-f
ive
peop
le a
re s
tand
ing
in a
cir
cle.
Star
ting
wit
h pe
rson
1,t
hey
coun
t of
f fr
om
1 to
7 a
nd t
hen
star
t ov
er w
ith
1.E
ach
pers
on w
ho s
ays
“7”
drop
s ou
t of
the
cir
cle.
Who
is t
he la
st p
erso
n le
ft?
num
ber
15
2.Fo
rty
peop
le s
tand
in a
cir
cle.
The
y co
unt
off
so t
hat
ever
y th
ird
pers
on d
rops
out
.Whi
ch t
wo
peop
le a
re t
he la
st o
nes
left
?13
th a
nd 2
8th
peop
le
3.O
nly
half
of
the
30 s
tude
nts
in
Shar
on’s
cla
ss c
an g
o on
a f
ield
tr
ip.S
haro
n ar
rang
es t
he b
oys
and
girl
s as
sho
wn.
The
y co
unt
off
from
1 t
o 9
and
ever
y ni
nth
pers
on d
rops
out
unt
il on
ly
15 p
eopl
e ar
e le
ft.W
ho g
ets
to
go o
n th
e fi
eld
trip
.th
e gi
rls
A g
rou
p o
f p
eop
le s
tan
d i
n a
cir
cle
and
cou
nt
off
1,2,
1,2,
1 an
d
so o
n.E
very
sec
ond
per
son
dro
ps
out.
Per
son
nu
mbe
r 1
is t
he
last
per
son
lef
t.
4.D
raw
a d
iagr
am t
o sh
ow w
hy t
he n
umbe
r of
peo
ple
in t
he
circ
le m
ust
be e
ven.
The
n,ex
plai
n yo
ur a
nsw
er.
If th
e nu
mbe
r is
odd
,per
son
1 w
ould
dro
p ou
t af
ter
the
first
rou
nd.
5.W
hen
the
coun
t re
turn
s to
per
son
num
ber
1 fo
r th
e fi
rst
tim
e,ho
w m
any
peop
le h
ave
drop
ped
out?
half
of t
he o
rigi
nal n
umbe
r
6.F
ind
the
num
ber
of p
eopl
e in
the
cir
cle
if t
he n
umbe
r is
be
twee
n 10
and
20.
Do
the
sam
e if
the
num
ber
is b
etw
een
30 a
nd 4
0.W
hat
can
you
conc
lude
abo
ut t
he o
rigi
nal
num
ber
of p
eopl
e?16
;32;
The
num
ber
mus
t be
a p
ower
of
2.
G
GG
G
GG
GG
GG
G
GG
G
GB
B
BB
B
BB
BB
BB
BB
B
B1
23
45
67
89
1011
1213
14
1516
1718
1920
2122
2324
2526
2728
2930
12
34
56
7
8 9 10
11
1213
1415
1617
18
19
20
2122
23
2425
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-2
3-2
Answers (Lesson 3-2)
© Glencoe/McGraw-Hill A8 Glencoe Algebra 1
Stu
dy
Gu
ide
an
d I
nte
rven
tion
Sol
ving
Equ
atio
ns b
y U
sing
Mul
tiplic
atio
n an
d D
ivis
ion
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-3
3-3
©G
lenc
oe/M
cGra
w-H
ill14
9G
lenc
oe A
lgeb
ra 1
Lesson 3-3
Solv
e U
sin
g M
ult
iplic
atio
nIf
eac
h si
de o
f an
equ
atio
n is
mul
tipl
ied
by t
he s
ame
num
ber,
the
resu
ltin
g eq
uati
on is
equ
ival
ent
to t
he g
iven
one
.You
can
use
the
pro
pert
y to
solv
e eq
uati
ons
invo
lvin
g m
ulti
plic
atio
n an
d di
visi
on.
Mul
tiplic
atio
n P
rope
rty
of E
qual
ityF
or a
ny n
umbe
rs a
, b, a
nd c
, if a
"b,
then
ac
"bc
.
Sol
ve 3
p"
1.
3p
"1
Orig
inal
equ
atio
n
p"
Rew
rite
each
mix
ed n
umbe
r as
an
impr
oper
frac
tion.
"p #
""
#M
ultip
ly e
ach
side
by
.
p"
Sim
plify
.
The
sol
utio
n is
.
3 % 7
3 % 7
2 % 73 % 2
2 % 77 % 2
2 % 7
3 % 27 % 2
1 % 21 % 2
1 % 21 % 2
Sol
ve !
n"
16.
#n
"16
Orig
inal
equ
atio
n
#4 "#
n #"
#4(
16)
Mul
tiply
eac
h si
de b
y #
4.
n"
#64
Sim
plify
.
The
sol
utio
n is
#64
.
1 % 41 % 4
1 % 4Ex
ampl
e1Ex
ampl
e1Ex
ampl
e2Ex
ampl
e2
Exer
cises
Exer
cises
Sol
ve e
ach
equ
atio
n.T
hen
ch
eck
you
r so
luti
on.
1."
#2
!6
2.m
"6
483.
p"
3
4.5
"60
5.#
k"
#2.
510
6.#
"!
5
7.#
1h
"4
!8.
#12
"#
k8
9."
1
10.#
3b
"5
!1
11.
m"
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12.
"#
!1
Wri
te a
n e
quat
ion
for
eac
h p
robl
em.T
hen
sol
ve t
he
equ
atio
n.
13.O
ne-f
ifth
of
a nu
mbe
r eq
uals
25.
Fin
d th
e nu
mbe
r.n
"25
;125
14.W
hat
num
ber
divi
ded
by 2
equ
als
#18
?"
!18
;!36
15.A
num
ber
divi
ded
by e
ight
equ
als
3.F
ind
the
num
ber.
"3;
24
16.O
ne a
nd a
hal
f ti
mes
a n
umbe
r eq
uals
6.F
ind
the
num
ber.
1n
"6;
41 % 2
n % 8
n % 2
1 % 5
1 % 41 % 4
p % 52 % 7
7 % 101 % 2
1 % 3
1 % 52 % 5
j % 33 % 2
8 % 31 % 2
5 % 8m % 8
1 % 4y % 12
3 % 51 % 5
1 % 8h % 3
©G
lenc
oe/M
cGra
w-H
ill15
0G
lenc
oe A
lgeb
ra 1
Solv
e U
sin
g D
ivis
ion
To s
olve
equ
atio
ns w
ith
mul
tipl
icat
ion
and
divi
sion
,you
can
als
ous
e th
e D
ivis
ion
Pro
pert
y of
Equ
alit
y.If
eac
h si
de o
f an
equ
atio
n is
div
ided
by
the
sam
enu
mbe
r,th
e re
sult
ing
equa
tion
is t
rue.
Div
isio
n P
rope
rty
of E
qual
ityF
or a
ny n
umbe
rs a
, b, a
nd c
, with
c(
0, if
a"
b, th
en
".
b % ca % c
Stu
dy
Gu
ide
and I
nte
rven
tion
(c
onti
nued
)
Sol
ving
Equ
atio
ns b
y U
sing
Mul
tiplic
atio
n an
d D
ivis
ion
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-3
3-3
Sol
ve 8
n"
64.
8n"
64O
rigin
al e
quat
ion
"D
ivid
e ea
ch s
ide
by 8
.
n"
8S
impl
ify.
The
sol
utio
n is
8.
64 % 88n % 8
Sol
ve !
5n"
60.
#5n
"60
Orig
inal
equ
atio
n
"D
ivid
e ea
ch s
ide
by #
5.
n"
#12
Sim
plify
.
The
sol
utio
n is
#12
.
60 % #5
#5n
% #5
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Sol
ve e
ach
equ
atio
n.T
hen
ch
eck
you
r so
luti
on.
1.3h
"#
42!
142.
8m"
162
3.#
3t"
51!
17
4.#
3r"
#24
85.
8k"
#64
!8
6.#
2m"
16!
8
7.12
h"
48.
#2.
4p"
7.2
!3
9.0.
5j"
510
10.#
25 "
5m!
511
.6m
"15
212
.#1.
5p"
#75
50
Wri
te a
n e
quat
ion
for
eac
h p
robl
em.T
hen
sol
ve t
he
equ
atio
n.
13.F
our
tim
es a
num
ber
equa
ls 6
4.F
ind
the
num
ber.
4n"
64;1
6
14.W
hat
num
ber
mul
tipl
ied
by #
4 eq
uals
#16
?!
4n"
!16
;4
15.A
num
ber
tim
es e
ight
equ
als
#36
.Fin
d th
e nu
mbe
r.8n
"!
36;!
41 % 2
1 % 2
1 % 3
Answers (Lesson 3-3)
© Glencoe/McGraw-Hill A9 Glencoe Algebra 1
An
swer
s
Skil
ls P
ract
ice
Sol
ving
Equ
atio
ns b
y U
sing
Mul
tiplic
atio
n an
d D
ivis
ion
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-3
3-3
©G
lenc
oe/M
cGra
w-H
ill15
1G
lenc
oe A
lgeb
ra 1
Lesson 3-3
Sol
ve e
ach
equ
atio
n.T
hen
ch
eck
you
r so
luti
on.
1.12
z"
108
92.
#7t
"49
!7
3.18
e"
#21
6!
124.
#22
"11
v!
2
5.#
6d"
#42
76.
96 "
#24
a!
4
7."
1664
8."
914
4
9.#
84 "
!25
210
.#"
#13
91
11.
"#
13!
5212
.31
"#
n!
186
13.#
6 "
z!
914
.q
"#
4!
14
15.
p"
#10
!18
16.
"4
17.#
0.4b
"5.
2!
1318
.1.6
m"
#4
!2.
5
Wri
te a
n e
quat
ion
for
eac
h p
robl
em.T
hen
sol
ve t
he
equ
atio
n.
19.T
he o
ppos
ite
of a
num
ber
is #
9.W
hat
is t
he n
umbe
r?!
n"
!9;
9
20.F
ourt
een
tim
es a
num
ber
is #
42.F
ind
the
num
ber.
14n
"!
42;!
3
21.E
ight
tim
es a
num
ber
equa
ls 1
28.W
hat
is t
he n
umbe
r?8n
"12
8;16
22.N
egat
ive
twel
ve t
imes
a n
umbe
r eq
uals
#13
2.F
ind
the
num
ber.
!12
n"
!13
2;11
23.N
egat
ive
eigh
teen
tim
es a
num
ber
is #
54.W
hat
is t
he n
umbe
r?!
18n
"!
54;3
24.O
ne s
ixth
of
a nu
mbe
r is
#17
.Fin
d th
e nu
mbe
r.n
"!
17;!
102
25.N
egat
ive
thre
e fi
fths
of
a nu
mbe
r is
#15
.Wha
t is
the
num
ber?
!n
"!
15;2
53 % 5
1 % 6
2 % 5a % 10
5 % 9
2 % 72 % 3
1 % 6t % 4
d % 7d % 3
a % 16c % 4
©G
lenc
oe/M
cGra
w-H
ill15
2G
lenc
oe A
lgeb
ra 1
Sol
ve e
ach
equ
atio
n.T
hen
ch
eck
you
r so
luti
on.
1.8j
"96
122.
#13
z"
#39
33.
#18
0 "
15m
!12
4.24
3 "
27c
95.
"#
8!
726.
#"
#8
96
7."
128.
"6
9."
4
10.#
1 "
#t
11.#
w"
#9
2412
.#s
"4
!20
13.#
3x"
!14
.a
"15
.h
"
16.5
n"
17.2
.5k
"20
818
.#3.
4e"
#3.
741.
1
19.#
1.7b
"2.
21!
1.3
20.0
.26p
"0.
104
0.4
21.4
.2q
"#
3.36
!0.
8
Wri
te a
n e
quat
ion
for
eac
h p
robl
em.T
hen
sol
ve t
he
equ
atio
n.
22.N
egat
ive
nine
tim
es a
num
ber
equa
ls #
117.
Fin
d th
e nu
mbe
r.!
9n"
!11
7;13
23.N
egat
ive
one
eigh
th o
f a
num
ber
is #
.Wha
t is
the
num
ber?
!n
"!
;6
24.F
ive
sixt
hs o
f a
num
ber
is #
.Fin
d th
e nu
mbe
r.n
"!
;!
25.2
.7 t
imes
a n
umbe
r eq
uals
8.3
7.W
hat
is t
he n
umbe
r?2.
7n"
8.37
;3.1
26.O
ne a
nd o
ne f
ourt
h ti
mes
a n
umbe
r is
one
and
one
thi
rd.W
hat
is t
he n
umbe
r?
1n
"1
;1
27.P
UB
LISH
ING
Tw
o un
its
of m
easu
re u
sed
in p
ublis
hing
are
the
pic
aan
d th
e po
int.
A p
ica
is o
ne s
ixth
of
an in
ch.T
here
are
12
poin
ts in
a p
ica,
so P
oint
s "
12 ·
Pic
as.H
ow m
any
pica
s ar
e eq
uiva
lent
to
108
poin
ts?
9 pi
cas
RO
LLER
CO
AST
ERS
For
Exe
rcis
es 2
8 an
d 2
9,u
se t
he
foll
owin
g in
form
atio
n.
Sup
erm
an t
he E
scap
ein
Cal
ifor
nia
is t
he f
aste
st r
olle
r co
aste
r in
the
wor
ld.R
ider
s fa
ll 41
5 fe
et in
7 s
econ
ds.S
peed
s re
ach
a m
axim
um o
f 10
0 m
iles
per
hour
.
28.I
f x
repr
esen
ts t
he a
vera
ge r
ate
of f
all o
f th
e ro
ller
coas
ter,
wri
te a
n ex
pres
sion
to
repr
esen
t th
e si
tuat
ion
(Hin
t:U
se t
he d
ista
nce
form
ula
d"
rt.)
7x"
415
29.W
hat
is t
he a
vera
ge r
ate
that
rid
ers
fall
in f
eet
per
seco
nd?
abou
t 59
.3 f
t/s
1 % 151 % 3
1 % 4
2 % 35 % 9
5 % 65 % 9
3 % 41 % 8
3 % 4
11 % 2011 % 4
11 % 1011 % 6
5 % 35 % 6
4 % 38 % 5
1 % 23 % 2
3 % 153 % 8
7 % 44 % 7
1 % 6q % 24
2 % 9g % 27
4 % 5a % 15
j % 12y % 9
Pra
ctic
e (A
vera
ge)
Sol
ving
Equ
atio
ns b
y U
sing
Mul
tiplic
atio
n an
d D
ivis
ion
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-3
3-3
Answers (Lesson 3-3)
© Glencoe/McGraw-Hill A10 Glencoe Algebra 1
Rea
din
g t
o L
earn
Math
emati
csS
olvi
ng E
quat
ions
by
Usi
ng M
ultip
licat
ion
and
Div
isio
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-3
3-3
©G
lenc
oe/M
cGra
w-H
ill15
3G
lenc
oe A
lgeb
ra 1
Lesson 3-3
Pre-
Act
ivit
yH
ow c
an e
quat
ion
s be
use
d t
o fi
nd
how
lon
g it
tak
es l
igh
t to
rea
chE
arth
?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 3-
3 at
the
top
of
page
135
in y
our
text
book
.
•In
the
equ
atio
n d
"rt
,sho
wn
in t
he in
trod
ucti
on,w
hat
num
ber
is u
sed
for
r? f
or d
?
5,87
0,00
0,00
0,00
0;31
1,11
0,00
0,00
0,00
0•
Wha
t eq
uati
on c
ould
you
use
to
find
the
tim
e it
tak
es li
ght
to r
each
Ear
thfr
om t
he f
arth
est
star
in t
he B
ig D
ippe
r?
5,87
0,00
0,00
0,00
0t"
821,
800,
000,
000,
000
Rea
din
g t
he
Less
on
Com
ple
te t
he
sen
ten
ce a
fter
eac
h e
quat
ion
to
tell
how
you
wou
ld s
olve
th
eeq
uat
ion
.
1."
16ea
ch s
ide
by
.
2.5x
"12
5ea
ch s
ide
by
,or
mul
tipl
y ea
ch s
ide
by
.
3.#
8k"
96D
ivid
e ea
ch s
ide
by
,or
mul
tipl
y ea
ch s
ide
by
.
4.E
xpla
in h
ow r
ewri
ting
4x
"2
as
x"
help
s yo
u so
lve
the
equa
tion
.
It m
akes
it e
asie
r fo
r yo
u to
see
wha
t nu
mbe
r yo
u ne
ed t
o m
ultip
ly b
y on
each
sid
e.
Hel
pin
g Y
ou
Rem
emb
er
5.O
ne w
ay t
o re
mem
ber
som
ethi
ng is
to
expl
ain
it t
o so
meo
ne e
lse.
Wri
te h
ow y
ou w
ould
ex
plai
n to
a c
lass
mat
e ho
w t
o so
lve
the
equa
tion
x
"12
.
Sam
ple
answ
er:M
ultip
ly e
ach
side
of
the
equa
tion
by t
he r
ecip
roca
l of
so y
ou c
an is
olat
e x
on t
he le
ft s
ide.
2 % 3
2 % 3
17 % 813 % 3
1 % 81 % 3
!%1 8%
!8
%1 5%5
Div
ide
7M
ultip
lyx % 7
©G
lenc
oe/M
cGra
w-H
ill15
4G
lenc
oe A
lgeb
ra 1
Dis
sect
ion
Puz
zles
:Mak
e th
e S
quar
eIn
a d
isse
ctio
n pu
zzle
,you
are
to
cut
apar
t on
e fi
gure
usi
ng o
nly
stra
ight
cut
s an
d th
en r
earr
ange
the
pie
ces
to m
ake
a ne
w f
igur
e.U
sual
ly t
he p
uzzl
e-so
lver
mus
t fi
gure
out
whe
re t
o m
ake
the
give
nnu
mbe
r of
cut
s.H
owev
er,f
or t
hese
puz
zles
,the
cut
line
s ar
e sh
own.
You
mus
t di
scov
er h
ow t
o re
arra
nge
the
piec
es.
Cu
t ap
art
each
fig
ure
.Th
en r
earr
ange
th
e p
iece
s to
for
m a
squ
are.
1. 2. 3. 4.H
int:
Cut
one
of
the
tria
ngle
s in
to t
wo
piec
es t
o m
ake
this
squ
are.
AA
AA
A
2x2x
2x
x
A
AA
A
AA
AA
BA
AA
A
B
2x2x
x
x
A
C D
A
C
B
B
D
AB
BB
B
A
BB
BB
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-3
3-3
Answers (Lesson 3-3)
© Glencoe/McGraw-Hill A11 Glencoe Algebra 1
An
swer
s
Stu
dy
Gu
ide
an
d I
nte
rven
tion
Sol
ving
Mul
ti-S
tep
Equ
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-4
3-4
©G
lenc
oe/M
cGra
w-H
ill15
5G
lenc
oe A
lgeb
ra 1
Lesson 3-4
Wo
rk B
ackw
ard
Wor
kin
g ba
ckw
ard
is o
ne o
f m
any
prob
lem
-sol
ving
str
ateg
ies
that
you
can
use
to s
olve
pro
blem
s.To
wor
k ba
ckw
ard,
star
t w
ith
the
resu
lt g
iven
at
the
end
of a
prob
lem
and
und
o ea
ch s
tep
to a
rriv
e at
the
beg
inni
ng n
umbe
r.
A n
um
ber
is d
ivid
edby
2,a
nd
th
en 8
is
subt
ract
ed f
rom
the
quot
ien
t.T
he
resu
lt i
s 16
.Wh
atis
th
e n
um
ber?
Solv
e th
e pr
oble
m b
y w
orki
ng b
ackw
ard.
The
fin
al n
umbe
r is
16.
Und
osu
btra
ctin
g 8
by a
ddin
g 8
to g
et 2
4.To
undo
div
idin
g 24
by
2,m
ulti
ply
24 b
y 2
to g
et 4
8.T
he o
rigi
nal n
umbe
r is
48.
A b
acte
ria
cult
ure
dou
bles
each
hal
f h
our.
Aft
er 3
hou
rs,t
her
e ar
e64
00 b
acte
ria.
How
man
y ba
cter
ia w
ere
ther
e to
beg
in w
ith
?
Solv
e th
e pr
oble
m b
y w
orki
ng b
ackw
ard.
The
bac
teri
a ha
ve g
row
n fo
r 3
hour
s.Si
nce
ther
ear
e 2
one-
half
hour
per
iods
in o
ne h
our,
in 3
hou
rsth
ere
are
6 on
e-ha
lf h
our
peri
ods.
Sinc
e th
eba
cter
ia c
ultu
re h
as g
row
n fo
r 6
tim
e pe
riod
s,it
has
doub
led
6 ti
mes
.Und
o th
e do
ublin
g by
halv
ing
the
num
ber
of b
acte
ria
6 ti
mes
.
6,40
0 !
!!
!!
!"
6,40
0 !
"10
0
The
re w
ere
100
bact
eria
to
begi
n w
ith.
1 % 641 % 2
1 % 21 % 2
1 % 21 % 2
1 % 2
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Sol
ve e
ach
pro
blem
by
wor
kin
g ba
ckw
ard
.
1.A
num
ber
is d
ivid
ed b
y 3,
and
then
4 is
add
ed t
o th
e qu
otie
nt.T
he r
esul
t is
8.F
ind
the
num
ber.
12
2.A
num
ber
is m
ulti
plie
d by
5,a
nd t
hen
3 is
sub
trac
ted
from
the
pro
duct
.The
res
ult
is 1
2.F
ind
the
num
ber.
3
3.E
ight
is s
ubtr
acte
d fr
om a
num
ber,
and
then
the
dif
fere
nce
is m
ulti
plie
d by
2.T
he r
esul
tis
24.
Fin
d th
e nu
mbe
r.20
4.T
hree
tim
es a
num
ber
plus
3 is
24.
Fin
d th
e nu
mbe
r.7
5.C
AR
REN
TAL
Ang
ela
rent
ed a
car
for
$29
.99
a da
y pl
us a
one
-tim
e in
sura
nce
cost
of
$5.0
0.H
er b
ill w
as $
124.
96.F
or h
ow m
any
days
did
she
ren
t th
e ca
r?4
days
6.M
ON
EYM
ike
wit
hdre
w a
n am
ount
of
mon
ey f
rom
his
ban
k ac
coun
t.H
e sp
ent
one
four
th f
or g
asol
ine
and
had
$90
left
.How
muc
h m
oney
did
he
wit
hdra
w?
$120
7.TE
LEV
ISIO
NS
In 1
999,
68%
of h
ouse
hold
s w
ith
TV
’s su
bscr
ibed
to
cabl
e T
V.If
8,0
00 m
ore
subs
crib
ers
are
adde
d to
the
num
ber
of h
ouse
hold
s w
ith
cabl
e,th
e to
tal n
umbe
r of
hous
ehol
ds w
ith
cabl
e T
V w
ould
be
67,6
00,0
00.H
ow m
any
hous
ehol
ds w
ere
ther
e w
ith
TV
in 1
999?
Sour
ce:W
orld
Alm
anac
99,4
00,0
00 h
ouse
hold
s
©G
lenc
oe/M
cGra
w-H
ill15
6G
lenc
oe A
lgeb
ra 1
Solv
e M
ult
i-St
ep E
qu
atio
ns
To s
olve
equ
atio
ns w
ith
mor
e th
an o
ne o
pera
tion
,oft
enca
lled
mu
lti-
step
equ
atio
ns,
undo
ope
rati
ons
by w
orki
ng b
ackw
ard.
Rev
erse
the
usu
alor
der
of o
pera
tion
s as
you
wor
k.
Sol
ve 5
x#
3 "
23.
5x'
3"
23O
rigin
al e
quat
ion.
5x'
3 #
3"
23 #
3S
ubtr
act 3
from
eac
h si
de.
5x"
20S
impl
ify.
"D
ivid
e ea
ch s
ide
by 5
.
x"
4S
impl
ify.
Sol
ve e
ach
equ
atio
n.T
hen
ch
eck
you
r so
luti
on.
1.5x
'2
"27
52.
6x'
9 "
273
3.5x
'16
"51
7
4.14
n#
8 "
343
5.0.
6x#
1.5
"1.
85.
56.
p#
4 "
1016
7.16
"23
68.
8 '
"13
209.
'3
"#
1380
10.
"10
!7
11.0
.2x
#8
"#
230
12.3
.2y
#1.
8 "
31.
5
13.#
4 "
414
.8 "
#12
'!
8015
.0 "
10y
#40
4
Wri
te a
n e
quat
ion
an
d s
olve
eac
h p
robl
em.
16.F
ind
thre
e co
nsec
utiv
e in
tege
rs w
hose
sum
is 9
6.n
#(n
#1)
#(n
#2)
"96
;31,
32,3
3
17.F
ind
two
cons
ecut
ive
odd
inte
gers
who
se s
um is
176
.n
#(n
#2)
"17
6;87
,89
18.
Fin
d th
ree
cons
ecut
ive
inte
gers
who
se s
um is
#93
.n
#(n
#1)
#(n
#2)
"!
93;!
32,!
31,!
30
k% #
43 % 7
7x#
(#1)
%%
#8
4b'
8%
#2
g% #
53n % 12
d#
12%
14
7 % 8
20 % 55x % 5
Stu
dy
Gu
ide
and I
nte
rven
tion
(c
onti
nued
)
Sol
ving
Mul
ti-S
tep
Equ
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-4
3-4
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 3-4)
© Glencoe/McGraw-Hill A12 Glencoe Algebra 1
Skil
ls P
ract
ice
Sol
ving
Mul
ti-S
tep
Equ
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-4
3-4
©G
lenc
oe/M
cGra
w-H
ill15
7G
lenc
oe A
lgeb
ra 1
Lesson 3-4
Sol
ve e
ach
pro
blem
by
wor
kin
g ba
ckw
ard
.
1.A
num
ber
is d
ivid
ed b
y 2,
and
then
the
quo
tien
t is
add
ed t
o 8.
The
res
ult
is 3
3.F
ind
the
num
ber.
50
2.T
wo
is s
ubtr
acte
d fr
om a
num
ber,
and
then
the
dif
fere
nce
is d
ivid
ed b
y 3.
The
res
ult
is30
.Fin
d th
e nu
mbe
r.92
3.A
num
ber
is m
ulti
plie
d by
2,a
nd t
hen
the
prod
uct
is a
dded
to
9.T
he r
esul
t is
49.
Wha
tis
the
num
ber?
20
4.A
LLO
WA
NC
EA
fter
Ric
ardo
rec
eive
d hi
s al
low
ance
for
the
wee
k,he
wen
t to
the
mal
lw
ith
som
e fr
iend
s.H
e sp
ent
half
of
his
allo
wan
ce o
n a
new
pap
erba
ck b
ook.
The
n he
boug
ht h
imse
lf a
sna
ck f
or $
1.25
.Whe
n he
arr
ived
hom
e,he
had
$5.
00 le
ft.H
ow m
uch
was
his
allo
wan
ce?
$12.
50
Sol
ve e
ach
equ
atio
n.T
hen
ch
eck
you
r so
luti
on.
5.5x
'3
"23
46.
4 "
3a#
146
7.2y
'5
"19
7
8.6
'5c
"#
29!
79.
8 #
5w"
#37
910
.18
#4v
"42
!6
11.
#8
"#
218
12.5
'"
1!
1613
.##
4 "
13!
51
14.#
'12
"#
711
415
.#
2 "
955
16.
'3
"#
1!
28
17.
q#
7 "
820
18.
g'
6 "
#12
!27
19.
z#
8 "
#3
2
20.
m'
2 "
65
21.
"3
1722
."
25
Wri
te a
n e
quat
ion
an
d s
olve
eac
h p
robl
em.
23.T
wic
e a
num
ber
plus
fou
r eq
uals
6.W
hat
is t
he n
umbe
r?2n
#4
"6;
1
24.S
ixte
en is
sev
en p
lus
thre
e ti
mes
a n
umbe
r.F
ind
the
num
ber.
16 "
7 #
3n;3
25.F
ind
two
cons
ecut
ive
inte
gers
who
se s
um is
35.
n#
(n#
1) "
35;1
7,18
26.F
ind
thre
e co
nsec
utiv
e in
tege
rs w
hose
sum
is 3
6.n
#(n
#1)
#(n
#2)
"36
;11
,12,
13
b'
1%
3c
#5
%4
4 % 5
5 % 22 % 3
3 % 4
w % 7a % 5
d % 6
h % 3x % 4
n % 3
©G
lenc
oe/M
cGra
w-H
ill15
8G
lenc
oe A
lgeb
ra 1
Sol
ve e
ach
pro
blem
by
wor
kin
g ba
ckw
ard
.
1.T
hree
is a
dded
to
a nu
mbe
r,an
d th
en t
he s
um is
mul
tipl
ied
by 4
.The
res
ult
is 1
6.F
ind
the
num
ber.
1
2.A
num
ber
is d
ivid
ed b
y 4,
and
the
quot
ient
is a
dded
to
3.T
he r
esul
t is
24.
Wha
t is
the
num
ber?
84
3.T
wo
is s
ubtr
acte
d fr
om a
num
ber,
and
then
the
dif
fere
nce
is m
ulti
plie
d by
5.T
he r
esul
tis
30.
Fin
d th
e nu
mbe
r.8
4.B
IRD
WA
TCH
ING
Whi
le M
iche
lle s
at o
bser
ving
bir
ds a
t a
bird
fee
der,
one
four
th o
f th
ebi
rds
flew
aw
ay w
hen
they
wer
e st
artl
ed b
y a
nois
e.T
wo
bird
s le
ft t
he f
eede
r to
go
toan
othe
r st
atio
ned
a fe
w f
eet
away
.Thr
ee m
ore
bird
s fl
ew in
to t
he b
ranc
hes
of a
nea
rby
tree
.Fou
r bi
rds
rem
aine
d at
the
fee
der.
How
man
y bi
rds
wer
e at
the
fee
der
init
ially
?12
Sol
ve e
ach
equ
atio
n.T
hen
ch
eck
you
r so
luti
on.
5.#
12n
#19
"77
!8
6.17
'3f
"14
!1
7.15
t'
4 "
493
8.'
6 "
2!
209.
'3
"15
!48
10.
#6
"#
212
11.
y#
"2
12.#
32 #
f"
#17
!25
13.8
#k
"#
432
14.
"1
!1
15.
"#
942
16.
"16
29
17.
#0.
5 "
2.5
2118
.2.5
g'
0.45
"0.
950.
219
.0.4
m#
0.7
"0.
222.
3
Wri
te a
n e
quat
ion
an
d s
olve
eac
h p
robl
em.
20.S
even
less
tha
n fo
ur t
imes
a n
umbe
r eq
uals
13.
Wha
t is
the
num
ber?
4n!
7 "
13;5
21.F
ind
two
cons
ecut
ive
odd
inte
gers
who
se s
um is
116
.n
#(n
#2)
"11
6;57
,59
22.F
ind
two
cons
ecut
ive
even
inte
gers
who
se s
um is
126
.n
#(n
#2)
"12
6;62
,64
23.F
ind
thre
e co
nsec
utiv
e od
d in
tege
rs w
hose
sum
is 1
17.
n#
(n#
2) #
(n#
4) "
117;
37,3
9,41
24.C
OIN
CO
LLEC
TIN
GJu
ng h
as a
tot
al o
f 92
coi
ns in
his
coi
n co
llect
ion.
Thi
s is
8 m
ore
than
thr
ee t
imes
the
num
ber
of q
uart
ers
in t
he c
olle
ctio
n.H
ow m
any
quar
ters
doe
s Ju
ngha
ve in
his
col
lect
ion?
28
x % 7
3k#
7%
515
#a
%3
r'
13%
12
3 % 83 % 5
7 % 81 % 8
1 % 2
b % 3d % #4
u % 5
Pra
ctic
e (A
vera
ge)
Sol
ving
Mul
ti-S
tep
Equ
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-4
3-4
Answers (Lesson 3-4)
© Glencoe/McGraw-Hill A13 Glencoe Algebra 1
An
swer
s
Rea
din
g t
o L
earn
Math
emati
csS
olvi
ng M
ulti-
Ste
p E
quat
ions
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-4
3-4
©G
lenc
oe/M
cGra
w-H
ill15
9G
lenc
oe A
lgeb
ra 1
Lesson 3-4
Pre-
Act
ivit
yH
ow c
an e
quat
ion
s be
use
d t
o es
tim
ate
the
age
of a
n a
nim
al?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 3-
4 at
the
top
of
page
142
in y
our
text
book
.
•W
rite
the
equ
atio
n 8
'12
a"
124
in w
ords
.
Eig
ht p
lus
twel
ve t
imes
aeq
uals
one
hun
dred
tw
enty
-fou
r.•
How
man
y op
erat
ions
are
invo
lved
in t
he e
quat
ion?
two
Rea
din
g t
he
Less
on
1.W
hat
does
the
phr
ase
undo
the
ope
rati
ons
mea
n to
you
? G
ive
an e
xam
ple.
Usi
ng t
he o
ppos
ite o
pera
tions
in t
he o
ppos
ite o
rder
und
oes
the
oper
atio
ns;s
ubtr
actio
n un
does
add
ition
.
2.a.
If w
e un
do o
pera
tion
s in
rev
erse
of
the
orde
r of
ope
rati
ons,
wha
t op
erat
ions
do
we
dofi
rst?
addi
tion
or s
ubtr
actio
n
b.W
hat
oper
atio
ns d
o w
e do
last
?m
ultip
licat
ion
or d
ivis
ion
3.Su
ppos
e yo
u w
ant
to s
olve
"
6.
a.W
hat
is t
he g
roup
ing
sym
bol i
n th
e eq
uati
on
"6?
the
frac
tion
bar
b.W
hat
is t
he f
irst
ste
p in
sol
ving
the
equ
atio
n?M
ultip
ly e
ach
side
by
5.
c.W
hat
is t
he n
ext
step
in s
olvi
ng t
he e
quat
ion?
Sub
trac
t 3
from
eac
h si
de.
4.W
rite
an
equa
tion
for
the
pro
blem
bel
ow.
Sev
entim
esk
min
usfiv
eeq
uals
nega
tive
fort
y-se
ven
7•
k!
5"
!47
Hel
pin
g Y
ou
Rem
emb
er
5.E
xpla
in w
hy w
orki
ng b
ackw
ard
is a
use
ful s
trat
egy
for
solv
ing
equa
tion
s.
Sam
ple
answ
er:Y
ou c
an u
ndo
the
oper
atio
ns t
o ge
t ba
ck t
o th
e va
lue
ofth
e va
riab
le t
hat
will
mak
e th
e eq
uatio
n tr
ue.T
hat
valu
e is
the
sol
utio
n.
x'
3%
5
x'
3%
5
©G
lenc
oe/M
cGra
w-H
ill16
0G
lenc
oe A
lgeb
ra 1
Con
secu
tive
Inte
ger
Pro
blem
sM
any
type
s of
pro
blem
s an
d pu
zzle
s in
volv
e th
e id
ea o
f co
nsec
utiv
ein
tege
rs.K
now
ing
how
to
repr
esen
t th
ese
inte
gers
alg
ebra
ical
ly c
anhe
lp t
o so
lve
the
prob
lem
.
Fin
d f
our
con
secu
tive
od
d i
nte
gers
wh
ose
sum
is
!80
.
An
odd
inte
ger
can
be w
ritt
en a
s 2n
'1,
whe
re n
is a
ny in
tege
r.If
2n
+ 1
is t
he f
irst
odd
inte
ger,
then
add
2 t
o ge
t th
e ne
xt la
rges
t od
din
tege
r,an
d so
on.
Now
wri
te a
n eq
uati
on t
o so
lve
this
pro
blem
.(2
n'
1) '
(2n
'3)
'(2
n'
5) '
(2n
'7)
"#
80
Wri
te a
n e
quat
ion
for
eac
h p
robl
em.T
hen
sol
ve.
1.C
ompl
ete
the
solu
tion
to
the
prob
lem
in t
he e
xam
ple.
!23
,!21
,!19
,!17
2.F
ind
thre
e co
nsec
utiv
e ev
en in
tege
rs w
hose
sum
is 1
32.
2n#
(2n
#2)
#(2
n#
4) "
132;
n"
21;4
2,44
,46
3.F
ind
two
cons
ecut
ive
inte
gers
who
se s
um is
19.
n#
(n#
1) "
19;9
,10
4.F
ind
two
cons
ecut
ive
inte
gers
who
se s
um is
100
.
n#
(n#
1) "
100;
no s
olut
ion
5.T
he le
sser
of
two
cons
ecut
ive
even
inte
gers
is 1
0 m
ore
than
on
e-ha
lf t
he g
reat
er.F
ind
the
inte
gers
.
2n"
10 #
(2n
#2)
;22
and
24
6.T
he g
reat
er o
f tw
o co
nsec
utiv
e ev
en in
tege
rs is
6 le
ss t
han
thre
e ti
mes
the
less
er.F
ind
the
inte
gers
.
2n#
2 "
3(2n
) !
6;4,
6
7.F
ind
four
con
secu
tive
inte
gers
suc
h th
at t
wic
e th
e su
m o
f th
e tw
o gr
eate
r in
tege
rs e
xcee
ds t
hree
tim
es t
he f
irst
by
91.
2[(n
#2)
#(n
#3)
] "
3n#
91;8
1,82
,83,
84
8.F
ind
a se
t of
fou
r co
nsec
utiv
e po
siti
ve in
tege
rs s
uch
that
the
gr
eate
st in
tege
r in
the
set
is t
wic
e th
e le
ast
inte
ger
in t
he s
et.
n#
3 "
2n;{
3,4,
5,6}
1 % 2
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-4
3-4
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 3-4)
© Glencoe/McGraw-Hill A14 Glencoe Algebra 1
Stu
dy
Gu
ide
an
d I
nte
rven
tion
Sol
ving
Equ
atio
ns w
ith t
he V
aria
ble
on E
ach
Sid
e
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-5
3-5
©G
lenc
oe/M
cGra
w-H
ill16
1G
lenc
oe A
lgeb
ra 1
Lesson 3-5
Var
iab
les
on
Eac
h S
ide
To s
olve
an
equa
tion
wit
h th
e sa
me
vari
able
on
each
sid
e,fi
rst
use
the
Add
itio
n or
the
Sub
trac
tion
Pro
pert
y of
Equ
alit
y to
wri
te a
n eq
uiva
lent
equa
tion
tha
t ha
s th
e va
riab
le o
n ju
st o
ne s
ide
of t
he e
quat
ion.
The
n so
lve
the
equa
tion
.
Sol
ve 5
y!
8 "
3y#
12.
5y#
8"
3y'
125y
#8
#3y
"3y
'12
#3y
2y#
8"
122y
#8
'8
"12
'8
2y"
20
"
y"
10
The
sol
utio
n is
10.20 % 2
2y % 2
Sol
ve !
11 !
3y"
8y#
1.
#11
#3y
"8y
'1
#11
#3y
'3y
"8y
'1
'3y
#11
"11
y'
1#
11 #
1 "
11y
'1
#1
#12
"11
y
"
#1
"y
The
sol
utio
n is
#1
.1 % 11
1 % 11
11y
% 11#
12%11
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Sol
ve e
ach
equ
atio
n.T
hen
ch
eck
you
r so
luti
on.
1.6
#b
"5b
'30
2.5y
#2y
"3y
'2
3.5x
'2
"2x
#10
!4
no s
olut
ion
!4
4.4n
#8
"3n
'2
5.1.
2x'
4.3
"2.
1 #
x 6.
4.4s
'6.
2 "
8.8s
#1.
8
10!
1
7.b
'4
"b
'88
8.k
#5
"k
#1
9.8
#5p
"4p
#1
224
81
10.4
b#
8 "
10 #
2b11
.0.2
x#
8 "
#2
#x
12.3
y#
1.8
"3y
#1.
8
35
all n
umbe
rs
13.#
4 #
3x"
7x#
614
.8 '
4k"
#10
'k
15.2
0 #
a "
10a
#2
!6
2
16.
n'
8 "
n'
217
.y
#8
"9
#y
18.#
4r'
5 "
5 #
4r
!36
17al
l num
bers
19.#
4 #
3x"
6x#
620
.18
#4k
"#
10 #
4k21
.12
'2y
"10
y#
12
no s
olut
ion
32 % 9
3 % 52 % 5
1 % 22 % 31 % 5
1 % 43 % 4
1 % 81 % 2
20 % 11
©G
lenc
oe/M
cGra
w-H
ill16
2G
lenc
oe A
lgeb
ra 1
Gro
up
ing
Sym
bo
lsW
hen
solv
ing
equa
tion
s th
at c
onta
in g
roup
ing
sym
bols
,fir
st u
seth
e D
istr
ibut
ive
Pro
pert
y to
elim
inat
e gr
oupi
ng s
ymbo
ls.T
hen
solv
e.
Sol
ve 4
(2a
!1)
"!
10(a
!5)
.
4(2a
#1)
"#
10(a
#5)
Orig
inal
equ
atio
n
8a#
4 "
#10
a'
50D
istr
ibut
ive
Pro
pert
y
8a#
4 '
10a
"#
10a
'50
'10
aA
dd 1
0ato
eac
h si
de.
18a
#4
"50
Sim
plify
.
18a
#4
'4
"50
'4
Add
4 to
eac
h si
de.
18a
"54
Sim
plify
.
"D
ivid
e ea
ch s
ide
by 1
8.
a"
3S
impl
ify.
The
sol
utio
n is
3.
Sol
ve e
ach
equ
atio
n.T
hen
ch
eck
you
r so
luti
on.
1.#
3(x
'5)
"3(
x#
1)2.
2(7
'3t
) "#
t3.
3(a
'1)
#5
"3a
#2
!2
!2
all n
umbe
rs
4.75
#9g
"5(
#4
'2g
)5.
5(f
'2)
"2(
3 #
f)6.
4(p
'3)
"36
5!
6
7.18
"3(
2c'
2)8.
3(d
#8)
"3d
9.
5(p
'3)
'9
"3(
p#
2) '
6
2no
sol
utio
n!
12
10.4
(b#
2) "
2(5
#b)
11.1
.2(x
#2)
"2
#x
12.
"
32
!2
13.
"14
.2(4
'2k
) '10
"k
15.2
(w#
1) '
4 "
4(w
'1)
!4
!6
!1
16.6
(n#
1) "
2(2n
'4)
17.2
[2 '
3(y
#1)
] "22
18.#
4(r
'2)
"4(
2 #
4r)
74
1
19.#
3(x
#8)
"24
20.4
(4 #
4k) "
#10
#16
k21
.6(2
#2y
) "5(
2y#
2)
0no
sol
utio
n1
1 % 3
2a'
5%
3a
#8
%12
#y
%8
3 '
y%
4
4 % 7
54 % 1818
a% 18St
udy
Gu
ide
and I
nte
rven
tion
(c
onti
nued
)
Sol
ving
Equ
atio
ns w
ith t
he V
aria
ble
on E
ach
Sid
e
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-5
3-5
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 3-5)
© Glencoe/McGraw-Hill A15 Glencoe Algebra 1
An
swer
s
Skil
ls P
ract
ice
Sol
ving
Equ
atio
ns w
ith t
he V
aria
ble
on E
ach
Sid
e
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-5
3-5
©G
lenc
oe/M
cGra
w-H
ill16
3G
lenc
oe A
lgeb
ra 1
Lesson 3-5
Just
ify
each
ste
p.
1.4k
#3
"2k
'5
4k#
3 #
2k"
2k'
5 #
2ka.
Sub
trac
t 2k
from
eac
h si
de.
2k#
3 "
5b.
Sim
plify
.2k
#3
'3
"5
'3
c.A
dd 3
to
each
sid
e.2k
"8
d.S
impl
ify.
"e.
Div
ide
each
sid
e by
2.
k"
4f.
Sim
plify
.
2.2(
8u'
2) "
3(2u
#7)
16u
'4
"6u
#21
a.D
istr
ibut
ive
Pro
pert
y16
u'
4 #
6u"
6u#
21 #
6ub.
Sub
trac
t 6u
from
eac
h si
de.
10u
'4
"#
21c.
Sim
plify
.10
u'
4 #
4 "
#21
#4
d.S
ubtr
act
4 fr
om e
ach
side
.10
u"
#25
e.S
impl
ify.
"f.
Div
ide
each
sid
e by
10.
u"
#2.
5g.
Sim
plify
.
Sol
ve e
ach
equ
atio
n.T
hen
ch
eck
you
r so
luti
on.
3.2m
'12
"3m
#31
434.
2h#
8 "
h'
1725
5.7a
#3
"3
#2a
6.4n
#12
"12
#4n
3
7.4x
#9
"7x
'12
!7
8.#
6y#
3 "
3 #
6yno
sol
utio
n
9.5
'3r
"5r
#19
1210
.#9
'8k
"7
'4k
4
11.8
q'
12 "
4(3
'2q
)al
l num
bers
12.3
(5j'
2) "
2(3j
#6)
!2
13.6
(#3v
'1)
"5(
#2v
#2)
214
.#7(
2b#
4) "
5(#
2b'
6)!
0.5
or !
15.3
(8 #
3t) "
5(2
't)
116
.2(3
u'
7) "
#4(
3 #
2u)
13
17.8
(2f
#2)
"7(
3f'
2)!
618
.5(#
6 #
3d) "
3(8
'7d
)!
1.5
or !
1
19.6
(w#
1) "
3(3w
'5)
!7
20.7
(#3y
'2)
"8(
3y#
2)
21.
v#
6 "
6 #
v9
22.
#x
"x
'!
27 % 2
7 % 85 % 8
1 % 22 % 3
2 % 3
2 % 3
1 % 21 % 2
2 % 3#25
%10
10u
% 10
8 % 22k % 2
©G
lenc
oe/M
cGra
w-H
ill16
4G
lenc
oe A
lgeb
ra 1
Sol
ve e
ach
equ
atio
n.T
hen
ch
eck
you
r so
luti
on.
1.5x
#3
"13
#3x
22.
#4c
#11
"4c
'21
!4
3.1
#s
"6
#6s
14.
14 '
5n"
#4n
'17
5.k
#3
"2
#k
46.
(6 #
z) "
z2
7.3(
#2
#3x
) "#
9x#
4no
sol
utio
n8.
4(4
#w
) "3(
2w'
2)1
9.9(
4b#
1) "
2(9b
'3)
10.3
(6 '
5y) "
2(#
5 '
4y)
!4
11.#
5x#
10 "
2 #
(x'
4)!
212
.6 '
2(3j
#2)
"4(
1 '
j)1
13.
t#
t"
3 '
tno
sol
utio
n14
.1.4
f'
1.1
"8.
3 #
f3
15.
x#
"x
'6
16.2
#z
"z
'9
!8
17.
(3g
#2)
"18
.(c
'1)
"(3
c#
5)7
19.
(5 #
2h) "
120
.(2
m#
16)
"(2
m'
4)!
7 all n
umbe
rs21
.3(d
#8)
#5
"9(
d'
2) '
1!
822
.2(a
#8)
'7
"5(
a'
2) #
3a#
19
23.T
wo
thir
ds o
f a
num
ber
redu
ced
by 1
1 is
equ
al t
o 4
mor
e th
an t
he n
umbe
r.F
ind
the
num
ber.
!45
24.F
ive
tim
es t
he s
um o
f a
num
ber
and
3 is
the
sam
e as
3 m
ulti
plie
d by
1 le
ss t
han
twic
eth
e nu
mbe
r.W
hat
is t
he n
umbe
r?18
25.N
UM
BER
TH
EORY
Tri
plin
g th
e gr
eate
r of
tw
o co
nsec
utiv
e ev
en in
tege
rs g
ives
the
sam
ere
sult
as
subt
ract
ing
10 f
rom
the
less
er e
ven
inte
ger.
Wha
t ar
e th
e in
tege
rs?
!8,
!6
26.G
EOM
ETRY
The
for
mul
a fo
r th
e pe
rim
eter
of
a re
ctan
gle
is P
"2!
'2w
,whe
re !
isth
e le
ngth
and
wis
the
wid
th.A
rec
tang
le h
as a
per
imet
er o
f 24
inch
es.F
ind
its
dim
ensi
ons
if it
s le
ngth
is 3
inch
es g
reat
er t
han
its
wid
th.
4.5
in.b
y 7.
5 in
.
1 % 31 % 9
1 % 4h % 2
1 % 4
1 % 61 % 3
3 % 4g % 6
1 % 2
1 % 83 % 4
5 % 61 % 2
1 % 62 % 3
3 % 25 % 2
5 % 6
1 % 23 % 4
1 % 2
1 % 3
Pra
ctic
e (A
vera
ge)
Sol
ving
Equ
atio
ns w
ith t
he V
aria
ble
on E
ach
Sid
e
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-5
3-5
Answers (Lesson 3-5)
© Glencoe/McGraw-Hill A16 Glencoe Algebra 1
Rea
din
g t
o L
earn
Math
emati
csS
olvi
ng E
quat
ions
with
the
Var
iabl
e on
Eac
h S
ide
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-5
3-5
©G
lenc
oe/M
cGra
w-H
ill16
5G
lenc
oe A
lgeb
ra 1
Lesson 3-5
Pre-
Act
ivit
yH
ow c
an a
n e
quat
ion
be
use
d t
o d
eter
min
e w
hen
tw
o p
opu
lati
ons
are
equ
al?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 3-
5 at
the
top
of
page
149
in y
our
text
book
.
In t
he e
quat
ion
12 !
7.6x
"6
!8x
,wha
t do
7.6
xan
d 8x
repr
esen
t?
7.6x
repr
esen
ts t
he in
crea
se (
in m
illio
ns)
in t
he n
umbe
r of
mal
e In
tern
et u
sers
,and
8x
repr
esen
ts t
he in
crea
se (
inm
illio
ns)
in t
he n
umbe
r of
fem
ale
Inte
rnet
use
rs.
Read
ing
the
Less
on
1.Su
ppos
e yo
u w
ant
to h
elp
a fr
iend
sol
ve 6
k!
7 "
3k#
8.W
hat
wou
ld y
ou a
dvis
e he
r to
do f
irst
? W
hy?
Sub
trac
t 3k
from
eac
h si
de;a
fter
she
doe
s th
at a
nd s
impl
ifies
,all
of t
heva
riab
les
will
be
on t
he le
ft s
ide.
2.W
hen
solv
ing
2(3x
#4)
"3(
x!
5),w
hy is
it h
elpf
ul f
irst
to
use
the
Dis
trib
utiv
e P
rope
rty
to r
emov
e th
e gr
oupi
ng s
ymbo
ls?
Onc
e yo
u ha
ve r
emov
ed th
e gr
oupi
ng s
ymbo
ls,y
ou c
an te
ll w
hat y
ou n
eed
to a
dd o
r su
btra
ct to
eac
h si
de to
get
all
of th
e va
riab
les
on o
ne s
ide.
3.O
n a
quiz
,Jas
on s
olve
d th
ree
equa
tion
s.H
is t
each
er s
aid
all t
he w
ork
was
cor
rect
,but
she
aske
d hi
m t
o w
rite
sho
rt s
ente
nces
to
tell
wha
t th
e so
luti
ons
wer
e.In
wha
t fo
llow
s,yo
u se
e th
e la
steq
uati
on in
his
wor
k fo
r ea
ch e
quat
ion.
Wri
te s
ente
nces
to
desc
ribe
the
solu
tion
s.
a.x
"#
4Th
e so
lutio
n is
!4.
b.6m
"6m
All
num
bers
are
sol
utio
ns.
c.12
"37
Ther
e ar
e no
sol
utio
ns.
4.In
Que
stio
n 3,
one
of t
he e
quat
ions
Jas
on s
olve
d w
as a
n id
enti
ty.W
hich
equ
atio
n w
as it
?E
xpla
in h
ow y
ou k
now
.
The
one
for
whi
ch t
he la
st s
tep
was
6m
"6m
;the
exp
ress
ions
on
the
left
and
righ
t si
des
are
the
sam
e.
Hel
ping
You
Rem
embe
r
5.A
n eq
uati
on w
ith
vari
able
s is
an
iden
tity
whe
n th
e eq
uati
on is
alw
ays
true
.In
othe
rw
ords
,the
exp
ress
ions
on
the
left
and
rig
ht s
ides
alw
ays
have
the
sam
e va
lue.
Loo
k up
the
wor
d id
enti
tyin
the
dic
tion
ary.
Wri
te a
ll th
e de
fini
tion
s th
at a
re s
imila
r to
the
mat
hem
atic
al d
efin
itio
n.S
ee s
tude
nts’
wor
k.
©G
lenc
oe/M
cGra
w-H
ill16
6G
lenc
oe A
lgeb
ra 1
Iden
titie
sA
n eq
uati
on t
hat
is t
rue
for
ever
y va
lue
of t
he v
aria
ble
is c
alle
d an
iden
tity
.Whe
n yo
u tr
y to
sol
ve a
n id
enti
ty,y
ou e
nd u
p w
ith
ast
atem
ent
that
is a
lway
s tr
ue.H
ere
is a
n ex
ampl
e.
Sol
ve 8
!(5
!6x
) "
3(1
#2x
).
8 #
(5 #
6x)
"3(
1 !
2x)
8 #
5 #
(#6x
)"
3(1
!2x
)
8 #
5 !
6x"
3 !
6x
3 !
6x"
3 !
6x
Sta
te w
het
her
eac
h e
quat
ion
is
an i
den
tity
.If
it i
s n
ot,f
ind
its
sol
uti
on.
1.2(
2 #
3x) "
3(3
!x)
!4
2.5(
m!
1) !
6 "
3(4
!m
) !(2
m#
1)
x"
#1
iden
tity
3.(5
t!
9) #
(3t
#13
) "
2(11
!t)
4.14
#(6
#3c
) "4c
#c
iden
tity
no s
olut
ion
5.3y
#2(
y!
19)
"9y
#3(
9 #
y)6.
3(3h
#1)
"4(
h!
3)
y"
#1
h"
3
7.U
se t
he t
rue
equa
tion
3x
#2
"3x
#2
to c
reat
e an
iden
tity
of
your
ow
n.
Sam
ple
answ
er:
6x!
4 "
2(3x
!2)
8.U
se t
he f
alse
equ
atio
n 1
"2
to c
reat
e an
equ
atio
n w
ith
no s
olut
ion.
Sam
ple
answ
er:
2x#
1 "
2x#
2
9.C
reat
e an
equ
atio
n w
hose
sol
utio
n is
x"
3.
Sam
ple
answ
er:
3x#
2(x
#1)
"20
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-5
3-5
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 3-5)
© Glencoe/McGraw-Hill A17 Glencoe Algebra 1
An
swer
s
Stu
dy
Gu
ide
an
d I
nte
rven
tion
Rat
ios
and
Pro
port
ions
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-6
3-6
©G
lenc
oe/M
cGra
w-H
ill16
7G
lenc
oe A
lgeb
ra 1
Lesson 3-6
Rat
ios
and
Pro
po
rtio
ns
A r
atio
is a
com
pari
son
of t
wo
num
bers
by
divi
sion
.The
rat
io
of x
to y
can
be e
xpre
ssed
as
xto
y,x
:yor
.R
atio
s ar
e us
ually
exp
ress
ed in
sim
ples
t fo
rm.
An
equa
tion
sta
ting
tha
t tw
o ra
tios
are
equ
al is
cal
led
a p
rop
orti
on.T
o de
term
ine
whe
ther
two
rati
os f
orm
a p
ropo
rtio
n,ex
pres
s bo
th r
atio
s in
sim
ples
t fo
rm o
r ch
eck
cros
s pr
oduc
ts.
x % y
Det
erm
ine
wh
eth
er t
he
rati
os
and
fo
rm a
pro
por
tion
.
"w
hen
expr
esse
d in
sim
ples
t fo
rm.
"w
hen
expr
esse
d in
sim
ples
t fo
rm.
The
rat
ios
and
form
a p
ropo
rtio
n
beca
use
they
are
equ
al w
hen
expr
esse
d in
sim
ples
t fo
rm.
12 % 1824 % 36
2 % 312 % 18
2 % 324 % 36
12 % 1824 % 36
Use
cro
ss p
rod
uct
s to
det
erm
ine
wh
eth
er
and
fo
rm a
pro
por
tion
.
!W
rite
the
prop
ortio
n.
10(4
5) !
18(2
5)C
ross
pro
duct
s
450
"45
0S
impl
ify.
The
cro
ss p
rodu
cts
are
equa
l,so
"
.
Sinc
e th
e ra
tios
are
equ
al,t
hey
form
apr
opor
tion
.
25 % 4510 % 18
25 % 4510 % 18
25 % 4510 % 18
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Use
cro
ss p
rod
uct
s to
det
erm
ine
wh
eth
er e
ach
pai
r of
rat
ios
form
s a
pro
por
tion
.
1.,
2.,
3.,
yes
nono
4.,
5.,
6.,
nono
yes
7.,
8.,
9.,
yes
yes
yes
10.2
:3,2
0:3
011
.5 t
o 9,
25 t
o 45
12.
,
yes
yes
yes
13.5
:5,3
0:2
014
.18
to 2
4,50
to
7515
.100
:75,
44:3
3
nono
yes
16.
,17
.,
18.
,
yes
yes
yes
0.45
% 0.9
0.1
% 0.2
6 % 81.
5%2
1 % 200.
05%
1
9 % 872 % 64
20 % 3014 % 21
9 % 1215 % 20
5% 10
00.
1%2
12 % 274 % 9
3 % 1612 % 32
15 % 2025 % 36
25 % 4910 % 20
10 % 155 % 8
16 % 321 % 2
©G
lenc
oe/M
cGra
w-H
ill16
8G
lenc
oe A
lgeb
ra 1
Solv
e Pr
opor
tion
sIf
a p
ropo
rtio
n in
volv
es a
var
iabl
e,yo
u ca
n us
e cr
oss
prod
ucts
to
solv
e
the
prop
orti
on.I
n th
e pr
opor
tion
"
,xan
d 13
are
cal
led
extr
emes
and
5 an
d 10
are
calle
d m
ean
s.In
a p
ropo
rtio
n,th
e pr
oduc
t of
the
ext
rem
es is
equ
al t
o th
e pr
oduc
t of
the
mea
ns.
Mea
ns-E
xtre
mes
Pro
pert
y of
Pro
port
ions
For
any
num
bers
a, b
, c,a
nd d
, if
", t
hen
ad"
bc.
Sol
ve
".
"O
rigin
al p
ropo
rtio
n
13(x
) "5(
10)
Cro
ss p
rodu
cts
13x
"50
Sim
plify
.
"D
ivid
e ea
ch s
ide
by 1
3.
x"
3S
impl
ify.
The
sol
utio
n is
3.
Sol
ve e
ach
pro
por
tion
.
1."
!12
2."
3."
10
4."
25.
"12
6."
1
7."
268.
"9.
"15
10.
"14
11.
"no
sol
utio
n12
."
!2
13.
"68
14.
"no
sol
utio
n15
."
6
Use
a p
rop
orti
on t
o so
lve
each
pro
blem
.
16. M
OD
ELS
To m
ake
a m
odel
of
the
Gua
delo
upe
Riv
er b
ed,H
erm
ie u
sed
1 in
ch o
f cl
ay f
or5
mile
s of
the
riv
er’s
act
ual l
engt
h.H
is m
odel
riv
er w
as 5
0 in
ches
long
.How
long
is t
heG
uade
loup
e R
iver
?25
0 m
i
17.E
DU
CA
TIO
NJo
sh f
inis
hed
24 m
ath
prob
lem
s in
one
hou
r.A
t th
at r
ate,
how
man
yho
urs
will
it t
ake
him
to
com
plet
e 72
pro
blem
s?3
h
12 % 92
' w
%6
24 % k12 % k
15 % 3a
#8
%12
#y
% 83
' y
%4
12 % x1.
5%
x4 % 12
4% b
#2
p % 245 % 8
1 % 218 % 3
3 % d18 % 54
9% y
'1
3 % 63x % 21
8 % x4 % 6
3 % 4x
'1
%4
0.5
%x
0.1
%2
3 % 55 % 3
1 % t2 % 8
#3
%x
11 % 13
11 % 1350 % 1313
x% 13
10 % 13x % 5
10 % 13x % 5
c % da % b
10 % 13x % 5
Stu
dy
Gu
ide
and I
nte
rven
tion
(c
onti
nued
)
Rat
ios
and
Pro
port
ions
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-6
3-6
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 3-6)
© Glencoe/McGraw-Hill A18 Glencoe Algebra 1
Skil
ls P
ract
ice
Rat
ios
and
Pro
port
ions
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-6
3-6
©G
lenc
oe/M
cGra
w-H
ill16
9G
lenc
oe A
lgeb
ra 1
Lesson 3-6
Use
cro
ss p
rod
uct
s to
det
erm
ine
wh
eth
er e
ach
pai
r of
rat
ios
form
s a
pro
por
tion
.W
rite
yes
or n
o.
1.,
yes
2.,
no
3.,
yes
4.,
yes
5.,
no6.
,ye
s
7.,
yes
8.,
no
Sol
ve e
ach
pro
por
tion
.If
nec
essa
ry,r
oun
d t
o th
e n
eare
st h
un
dre
dth
.
9."
710
."
15
11.
"6
12.
"18
13.
"10
14.
"3
15.
"21
16.
"18
17.
"8
18.
"63
19.
"42
20.
"44
21.
"13
22.
"48
23.
"16
24.
"60
25.B
OA
TIN
GH
ue’s
boa
t us
ed 5
gal
lons
of
gaso
line
in 4
hou
rs.A
t th
is r
ate,
how
man
yga
llons
of
gaso
line
will
the
boa
t us
e in
10
hour
s?12
.5 g
al
11 % 3022 % x
s % 844 % 21
20 % g5 % 12
27 % 399 % c
n % 6011 % 15
30 % m10 % 14
1 % 97 % b
6 % f42 % 56
y % 696 % 23
36 % s12 % 7
35 % 215 % e
3 % 56 % z
1 % 63 % a
15 % 109 % g
3 % 95 % b
2 % 141 % a
50 % 8512 % 17
21 % 983 % 14
26 % 3813 % 19
42 % 907 % 16
72 % 818 % 9
24 % 286 % 7
7 % 115 % 9
20 % 254 % 5
©G
lenc
oe/M
cGra
w-H
ill17
0G
lenc
oe A
lgeb
ra 1
Use
cro
ss p
rod
uct
s to
det
erm
ine
wh
eth
er e
ach
pai
r of
rat
ios
form
s a
pro
por
tion
.W
rite
yes
or n
o.
1.,
no2.
,no
3.,
yes
4.,
yes
5.,
yes
6.,
yes
7.,
yes
8.,
no9.
,no
Sol
ve e
ach
pro
por
tion
.If
nec
essa
ry,r
oun
d t
o th
e n
eare
st h
un
dre
dth
.
10.
"9
11.
"68
12.
"5
13.
"7
14.
"18
15.
"16
16.
"12
17.
"77
18.
"1
19.
"12
220
."
2421
."
7
22.
"10
23.
"3
24.
"3
25.
"1
26.
"2.
8827
."
1.02
28.
"7
29.
"2
30.
"5
31.
"32
."
333
."
4
34.P
AIN
TIN
GY
sidr
a pa
ints
a r
oom
tha
t ha
s 40
0 sq
uare
fee
t of
wal
l spa
ce in
2ho
urs.
At
this
rat
e,ho
w lo
ng w
ill it
tak
e he
r to
pai
nt a
roo
m t
hat
has
720
squa
re f
eet
of w
all
spac
e?4
h
35.V
AC
ATI
ON
PLA
NS
Wal
ker
is p
lann
ing
a su
mm
er v
acat
ion.
He
wan
ts t
o vi
sit
Petr
ifie
dN
atio
nal F
ores
t an
d M
eteo
r C
rate
r,A
rizo
na,t
he 5
0,00
0-ye
ar-o
ld im
pact
sit
e of
a la
rge
met
eor.
On
a m
ap w
ith
a sc
ale
whe
re 2
inch
es e
qual
s 75
mile
s,th
e tw
o ar
eas
are
abou
t
1in
ches
apa
rt.W
hat
is t
he d
ista
nce
betw
een
Petr
ifie
d N
atio
nal F
ores
t an
d M
eteo
r
Cra
ter?
abou
t 56
.25
mi
1 % 2
1 % 2
1 % 24 % 7x
#2
%6
3 % 75 % 7
r'
2%
72 % 3
x'
1%
45 % 12
2 % 4m
#1
%8
2% y
'6
3 % 1214 % 6
7% a
#4
3% 0.
516 % n
12 % b3
% 0.72
7% 1.
61v
% 0.23
3 % 45 % 8
m % 63 % 5
5 % 63 % q
2 % 78 % c
7 % 9
2 % a14 % 49
6 % 4g % 16
12 % h6 % 61
z % 173 % 51
35 % x5 % 11
10 % 602 % y
48 % 9y % 3
27 % 162
3 % u4 % w
28 % 49
k % 740 % 56
34 % 23v % 46
30 % 545 % a
3.9
% 0.9
7.6
% 1.8
2.9
% 2.4
1.7
% 1.2
7.14
% 10.9
23.
4% 5.
2
1 % 61.
5%9
72 % 818 % 9
108
% 9912 % 11
36 % 4818 % 24
15 % 663 % 11
52 % 487 % 6
Pra
ctic
e (A
vera
ge)
Rat
ios
and
Pro
port
ions
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-6
3-6
Answers (Lesson 3-6)
© Glencoe/McGraw-Hill A19 Glencoe Algebra 1
An
swer
s
Rea
din
g t
o L
earn
Math
emati
csR
atio
s an
d P
ropo
rtio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-6
3-6
©G
lenc
oe/M
cGra
w-H
ill17
1G
lenc
oe A
lgeb
ra 1
Lesson 3-6
Pre-
Act
ivit
yH
ow a
re r
atio
s u
sed
in
rec
ipes
?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 3-
6 at
the
top
of
page
155
in y
our
text
book
.
•H
ow m
any
serv
ings
of
hone
y fr
ozen
yog
urt
are
mad
e by
thi
s re
cipe
?4
serv
ings
•H
ow m
any
reci
pes
wou
ld b
e ne
eded
to
mak
e en
ough
hon
ey f
roze
n yo
gurt
for
all t
he s
tude
nts
in y
our
clas
s?S
ee s
tude
nts’
wor
k.
Rea
din
g t
he
Less
on
1.C
ompl
ete
the
follo
win
g se
nten
ce.
A r
atio
is a
com
pari
son
of t
wo
num
bers
by
.
2.D
escr
ibe
two
way
s to
dec
ide
whe
ther
the
sen
tenc
e "
is a
pro
port
ion.
Exp
ress
the
rat
ios
in s
impl
est
form
to
see
if th
ey a
re e
qual
.Che
ck t
o se
ew
heth
er t
he c
ross
pro
duct
s ar
e eq
ual.
3.Fo
r ea
ch p
ropo
rtio
n,te
ll w
hat
the
extr
emes
are
and
wha
t th
e m
eans
are
.
a."
Ext
rem
es:
Mea
ns:
b."
Ext
rem
es:
Mea
ns:
4.A
jet
flyi
ng a
t a
stea
dy s
peed
tra
vele
d 82
5 m
iles
in 2
hou
rs.I
f yo
u so
lved
the
pro
port
ion
",w
hat
wou
ld t
he a
nsw
er t
ell y
ou a
bout
the
jet?
how
far
the
jet
trav
eled
in 1
.5 h
Hel
pin
g Y
ou
Rem
emb
er
5.W
rite
how
you
wou
ld e
xpla
in s
olvi
ng a
pro
port
ion
to a
fri
end
who
mis
sed
Les
son
3-6.
Use
cro
ss p
rodu
cts.
Wri
te a
n eq
uatio
n w
ith t
he p
rodu
ct o
f th
e ex
trem
eson
the
left
sid
e an
d th
e pr
oduc
t of
the
mea
ns o
n th
e ri
ght
side
.The
nso
lve
this
sec
ond
equa
tion.
x% 1.
582
5%
2
8 an
d 12
6 an
d 16
12 % 166 % 8
35 a
nd 6
14 a
nd 1
56 % 15
14 % 35
8 % 202 % 5divi
sion
©G
lenc
oe/M
cGra
w-H
ill17
2G
lenc
oe A
lgeb
ra 1
Ang
les
of a
Tri
angl
eIn
geo
met
ry,m
any
stat
emen
ts a
bout
phy
sica
l spa
ce a
re p
rove
n to
be
true
.Suc
h st
atem
ents
are
cal
led
theo
rem
s.H
ere
are
two
exam
ples
of
geom
etri
c th
eore
ms.
a.T
he s
um o
f th
e m
easu
res
of t
he a
ngle
s of
a t
rian
gle
is 1
80°.
b.If
tw
o si
des
of a
tri
angl
e ha
ve e
qual
mea
sure
,the
n th
e tw
o an
gles
oppo
site
tho
se s
ides
als
o ha
ve e
qual
mea
sure
.
For
eac
h o
f th
e tr
ian
gles
,wri
te a
n e
quat
ion
an
d t
hen
sol
ve f
or x
.(A
tic
k m
ark
on
two
or m
ore
sid
es o
f a
tria
ngl
e in
dic
ates
th
at t
he
sid
es h
ave
equ
al m
easu
re.)
1.x
"60
)2.
x"
45)
3.x
"45
)4.
x"
20)
5.x
"22
.5)
6.x
"10
)
7.x
"33
)8.
x"
100)
9.x
"60
)10
.x
"50
)
11.T
wo
angl
es o
f a
tria
ngle
hav
e th
e sa
me
12.T
he m
easu
re o
f on
e an
gle
of a
tri
angl
e is
m
easu
re.T
he s
um o
f th
e m
easu
res
of
twic
e th
e m
easu
re o
f a
seco
nd a
ngle
.The
th
ese
angl
es is
one
-hal
f th
e m
easu
re o
f m
easu
re o
f th
e th
ird
angl
e is
12
less
tha
n th
e th
ird
angl
e.F
ind
the
mea
sure
s of
th
e su
m o
f th
e ot
her
two.
Fin
d th
e th
e an
gles
of
the
tria
ngle
.m
easu
res
of t
he a
ngle
s of
the
tri
angl
e.30
),30
),12
0)64
),32
),84
)
x2x
30°
x
40°
x
x #
15°
3 x
x '
30°
90°4 x
5x
5x
2xx
x '
30°
x5x
' 1
0°
90°
x
90°
45°
x70
°
50°
x
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-6
3-6
Answers (Lesson 3-6)
© Glencoe/McGraw-Hill A20 Glencoe Algebra 1
Stu
dy
Gu
ide
an
d I
nte
rven
tion
Per
cent
of
Cha
nge
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-7
3-7
©G
lenc
oe/M
cGra
w-H
ill17
3G
lenc
oe A
lgeb
ra 1
Lesson 3-7
Perc
ent
of
Ch
ang
eW
hen
an in
crea
se o
r de
crea
se in
an
amou
nt is
exp
ress
ed a
s a
perc
ent,
the
perc
ent
is c
alle
d th
e p
erce
nt
of c
han
ge.I
f th
e ne
w n
umbe
r is
gre
ater
tha
n th
eor
igin
al n
umbe
r,th
e pe
rcen
t of
cha
nge
is a
per
cen
t of
in
crea
se.I
f th
e ne
w n
umbe
r is
less
than
the
ori
gina
l num
ber,
the
perc
ent
of c
hang
e is
the
per
cen
t of
dec
reas
e.
Fin
d t
he
per
cen
t of
in
crea
se.
orig
inal
:48
new
:60
Fir
st,s
ubtr
act
to f
ind
the
amou
nt o
fin
crea
se.T
he a
mou
nt o
f in
crea
se is
60
#48
"12
.T
hen
find
the
per
cent
of
incr
ease
by
usin
gth
e or
igin
al n
umbe
r,48
,as
the
base
.
"P
erce
nt p
ropo
rtio
n
12(1
00)
"48
(r)
Cro
ss p
rodu
cts
1200
"48
rS
impl
ify.
"D
ivid
e ea
ch s
ide
by 4
8.
25 "
rS
impl
ify.
The
per
cent
of
incr
ease
is 2
5%.
48r
% 4812
00%
48
r% 10
012 % 48
Fin
d t
he
per
cen
t of
dec
reas
e.or
igin
al:3
0n
ew:2
2
Fir
st,s
ubtr
act
to f
ind
the
amou
nt o
fde
crea
se.T
he a
mou
nt o
f de
crea
se is
30
#22
"8.
The
n fi
nd t
he p
erce
nt o
f de
crea
se b
y us
ing
the
orig
inal
num
ber,
30,a
s th
e ba
se.
"P
erce
nt p
ropo
rtio
n
8(10
0) "
30(r
)C
ross
pro
duct
s
800
"30
rS
impl
ify.
"D
ivid
e ea
ch s
ide
by 3
0.
26"
rS
impl
ify.
The
per
cent
of
decr
ease
is 2
6%
,or
abou
t27
%.
2 % 3
2 % 3
30r
% 3080
0% 30
r% 10
08 % 30
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Sta
te w
het
her
eac
h p
erce
nt
of c
han
ge i
s a
per
cen
t of
in
crea
se o
r a
per
cen
t of
dec
reas
e.T
hen
fin
d e
ach
per
cen
t of
ch
ange
.Rou
nd
to
the
nea
rest
wh
ole
per
cen
t.
1.or
igin
al:5
02.
orig
inal
:90
3.or
igin
al:4
5ne
w:8
0ne
w:1
00ne
w:2
0in
crea
se;6
0%in
crea
se:1
1%de
crea
se;5
6%
4.or
igin
al:7
7.5
5.or
igin
al:1
406.
orig
inal
:135
new
:62
new
:150
new
:90
decr
ease
;20%
incr
ease
:7%
decr
ease
;33%
7.or
igin
al:1
208.
orig
inal
:90
9.or
igin
al:2
7.5
new
:180
new
:270
new
:25
incr
ease
;50%
incr
ease
:200
%de
crea
se;9
%
10.o
rigi
nal:
8411
.ori
gina
l:12
.512
.ori
gina
l:25
0ne
w:9
8ne
w:1
0ne
w:5
00in
crea
se;1
7%de
crea
se:2
0%in
crea
se;1
00%
©G
lenc
oe/M
cGra
w-H
ill17
4G
lenc
oe A
lgeb
ra 1
Solv
e Pr
ob
lem
sD
isco
unte
d pr
ices
and
pri
ces
incl
udin
g ta
x ar
e ap
plic
atio
ns o
f pe
rcen
tof
cha
nge.
Dis
coun
t is
the
am
ount
by
whi
ch t
he r
egul
ar p
rice
of
an it
em is
red
uced
.Thu
s,th
e di
scou
nted
pri
ce is
an
exam
ple
of p
erce
nt o
f de
crea
se.S
ales
tax
is a
mou
nt t
hat
is a
dded
to t
he c
ost
of a
n it
em,s
o th
e pr
ice
incl
udin
g ta
x is
an
exam
ple
of p
erce
nt o
f in
crea
se.
A c
oat
is o
n s
ale
for
25%
off
th
e or
igin
al p
rice
.If
the
orig
inal
pri
ceof
th
e co
at i
s $7
5,w
hat
is
the
dis
cou
nte
d p
rice
?
The
dis
coun
t is
25%
of
the
orig
inal
pri
ce.
25%
of
$75
"0.
25 !
7525
% "
0.25
"18
.75
Use
a c
alcu
lato
r.
Subt
ract
$18
.75
from
the
ori
gina
l pri
ce.
$75
#$1
8.75
"$5
6.25
The
dis
coun
ted
pric
e of
the
coa
t is
$56
.25.
Fin
d t
he
fin
al p
rice
of
each
ite
m.W
hen
a d
isco
un
t an
d a
sal
es t
ax a
re l
iste
d,
com
pu
te t
he
dis
cou
nt
pri
ce b
efor
e co
mp
uti
ng
the
tax.
1.C
ompa
ct d
isc:
$16
2.T
wo
conc
ert
tick
ets:
$28
3.A
irlin
e ti
cket
:$24
8.00
Dis
coun
t:15
%St
uden
t di
scou
nt:2
8%Su
pera
ir d
isco
unt:
33%
$13.
60$2
0.16
$166
.16
4.Sh
irt:
$24.
005.
CD
pla
yer:
$142
.00
6.C
eleb
rity
cal
enda
r:$1
0.95
Sale
s ta
x:4%
Sale
s ta
x:5.
5%Sa
les
tax:
7.5%
$24.
96$1
49.8
1$1
1.77
7.C
lass
rin
g:$8
9.00
8.So
ftw
are:
$44.
009.
Vid
eo r
ecor
der:
$110
.95
Gro
up d
isco
unt:
17%
Dis
coun
t:21
%D
isco
unt:
20%
Sale
s ta
x:5%
Sale
s ta
x:6%
Sale
s ta
x:5%
$77.
56$3
6.85
$93.
20
10.V
IDEO
ST
he o
rigi
nal s
ellin
g pr
ice
of a
new
spo
rts
vide
o w
as $
65.0
0.D
ue t
o th
e de
man
dth
e pr
ice
was
incr
ease
d to
$87
.75.
Wha
t w
as t
he p
erce
nt o
f in
crea
se o
ver
the
orig
inal
pric
e?35
%
11.S
CH
OO
LA
hig
h sc
hool
pap
er in
crea
sed
its
sale
s by
75%
whe
n it
ran
an
issu
e fe
atur
ing
a co
ntes
t to
win
a c
lass
par
ty.B
efor
e th
e co
ntes
t is
sue,
10%
of
the
scho
ol’s
800
stu
dent
sbo
ught
the
pap
er.H
ow m
any
stud
ents
bou
ght
the
cont
est
issu
e?14
0 st
uden
ts
12.B
ASE
BA
LLB
aseb
all t
icke
ts c
ost
$15
for
gene
ral a
dmis
sion
or
$20
for
box
seat
s.T
hesa
les
tax
on e
ach
tick
et is
8%
,and
the
mun
icip
al t
ax o
n ea
ch t
icke
t is
an
addi
tion
al 1
0%of
the
bas
e pr
ice.
Wha
t is
the
fin
al c
ost
of e
ach
type
of
tick
et?
$17.
70;$
23.6
0
Stu
dy
Gu
ide
and I
nte
rven
tion
(c
onti
nued
)
Per
cent
of
Cha
nge
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-7
3-7
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 3-7)
© Glencoe/McGraw-Hill A21 Glencoe Algebra 1
An
swer
s
Skil
ls P
ract
ice
Per
cent
of
Cha
nge
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-7
3-7
©G
lenc
oe/M
cGra
w-H
ill17
5G
lenc
oe A
lgeb
ra 1
Lesson 3-7
Sta
te w
het
her
eac
h p
erce
nt
of c
han
ge i
s a
per
cen
t of
in
crea
se o
r a
per
cen
t of
dec
reas
e.T
hen
fin
d e
ach
per
cen
t of
ch
ange
.Rou
nd
to
the
nea
rest
wh
ole
per
cen
t.
1.or
igin
al:2
52.
orig
inal
:50
new
:10
new
:75
decr
ease
;60%
incr
ease
;50%
3.or
igin
al:5
54.
orig
inal
:25
new
:50
new
:28
decr
ease
;9%
incr
ease
;12%
5.or
igin
al:5
06.
orig
inal
:90
new
:30
new
:95
decr
ease
;40%
incr
ease
;6%
7.or
igin
al:4
88.
orig
inal
:60
new
:60
new
:45
incr
ease
;25%
decr
ease
;25%
Fin
d t
he
tota
l p
rice
of
each
ite
m.
9.dr
ess:
$69.
0010
.bin
der:
$14.
50ta
x:5%
tax:
7%$7
2.45
$15.
5211
.har
dcov
er b
ook:
$28.
9512
.gro
ceri
es:$
47.5
2ta
x:6%
tax:
3%$3
0.69
$48.
9513
.fill
er p
aper
:$6.
0014
.sho
es:$
65.0
0ta
x:6.
5%ta
x:4%
$6.3
9$6
7.60
15.b
aske
tbal
l:$1
7.00
16.c
once
rt t
icke
ts:$
48.0
0ta
x:6%
ta
x:7.
5%$1
8.02
$51.
60
Fin
d t
he
dis
cou
nte
d p
rice
of
each
ite
m.
17.b
ackp
ack:
$56.
2518
.mon
itor
:$15
0.00
disc
ount
:20%
disc
ount
:50%
$45.
00$7
5.00
19.C
D:$
15.9
920
.shi
rt:$
25.5
0di
scou
nt:2
0%di
scou
nt:4
0%$1
2.79
$15.
3021
.sle
epin
g ba
g:$1
2522
.cof
fee
mak
er:$
102.
00di
scou
nt:2
5%di
scou
nt:4
5%$9
3.75
$56.
10
©G
lenc
oe/M
cGra
w-H
ill17
6G
lenc
oe A
lgeb
ra 1
Sta
te w
het
her
eac
h p
erce
nt
of c
han
ge i
s a
per
cen
t of
in
crea
se o
r a
per
cen
t of
dec
reas
e.T
hen
fin
d e
ach
per
cen
t of
ch
ange
.Rou
nd
to
the
nea
rest
wh
ole
per
cen
t.
1.or
igin
al:1
82.
orig
inal
:140
3.or
igin
al:2
00ne
w:1
0ne
w:1
60ne
w:3
20de
crea
se;4
4%in
crea
se;1
4%in
crea
se;6
0%4.
orig
inal
:10
5.or
igin
al:7
66.
orig
inal
:128
new
:25
new
:60
new
:120
incr
ease
;150
%de
crea
se;2
1%de
crea
se;6
%7.
orig
inal
:15
8.or
igin
al:9
8.6
9.or
igin
al:5
8.8
new
:35.
5ne
w:6
4ne
w:6
5.7
incr
ease
;137
%de
crea
se;3
5%in
crea
se;1
2%
Fin
d t
he
tota
l p
rice
of
each
ite
m.
10.c
oncr
ete
bloc
ks:$
95.0
011
.cri
b:$2
40.0
012
.jac
ket:
$125
.00
tax:
6%ta
x:6.
5%ta
x:5.
5%$1
00.7
0$2
55.6
0$1
31.8
813
.cla
ss r
ing:
$325
.00
14.b
lank
et:$
24.9
915
.kit
e:$1
8.90
tax:
6%ta
x:7%
tax:
5%$3
44.5
0$2
6.74
$19.
85
Fin
d t
he
dis
cou
nte
d p
rice
of
each
ite
m.
16.d
ry c
lean
ing:
$25.
0017
.com
pute
r ga
me:
$49.
9918
.lug
gage
:$18
5.00
disc
ount
:15%
disc
ount
:25%
disc
ount
:30%
$21.
25$3
7.49
$129
.50
19.s
tati
oner
y:$1
2.95
20.p
resc
ript
ion
glas
ses:
$149
21.p
air
of s
hort
s:$2
4.99
di
scou
nt:1
0%di
scou
nt:2
0%di
scou
nt:4
5%$1
1.66
$119
.20
$13.
74
Fin
d t
he
fin
al p
rice
of
each
ite
m.
22.t
elev
isio
n:$3
75.0
023
.DV
D p
laye
r:$2
69.0
024
.pri
nter
:$25
5.00
disc
ount
:25%
disc
ount
:20%
disc
ount
:30%
tax:
6%ta
x:7%
tax:
5.5%
$298
.13
$230
.26
$188
.32
25.I
NV
ESTM
ENTS
The
pri
ce p
er s
hare
of
an in
tern
et-r
elat
ed s
tock
dec
reas
ed f
rom
$90
per
shar
e to
$36
per
sha
re e
arly
in 2
001.
By
wha
t pe
rcen
t di
d th
e pr
ice
of t
he s
tock
decr
ease
?60
%
26.H
EATI
NG
CO
STS
Cus
tom
ers
of a
uti
lity
com
pany
rec
eive
d no
tice
s in
the
ir m
onth
ly b
ills
that
hea
ting
cos
ts f
or t
he a
vera
ge c
usto
mer
had
incr
ease
d 12
5% o
ver
last
yea
r be
caus
eof
an
unus
ually
sev
ere
win
ter.
In J
anua
ry o
f la
st y
ear,
the
Gar
cia’
s pa
id $
120
for
heat
ing.
Wha
t sh
ould
the
y ex
pect
to
pay
this
Jan
uary
if t
heir
bill
incr
ease
d by
125
%?
$270
Pra
ctic
e (A
vera
ge)
Per
cent
of
Cha
nge
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-7
3-7
Answers (Lesson 3-7)
© Glencoe/McGraw-Hill A22 Glencoe Algebra 1
Rea
din
g t
o L
earn
Math
emati
csP
erce
nt o
f C
hang
e
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-7
3-7
©G
lenc
oe/M
cGra
w-H
ill17
7G
lenc
oe A
lgeb
ra 1
Lesson 3-7
Pre-
Act
ivit
yH
ow c
an p
erce
nts
des
crib
e gr
owth
ove
r ti
me?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 3-
7 at
the
top
of
page
160
in y
our
text
book
.
•H
ow m
any
area
cod
es w
ere
in u
se in
194
7?84
are
a co
des
•H
ow m
any
mor
e ar
ea c
odes
wer
e in
use
in 1
999?
201
area
cod
es
Read
ing
the
Less
on
1.If
you
use
(or
igin
al a
mou
nt)
— (
new
am
ount
) to
fin
d th
e ch
ange
for
a p
erce
nt o
f ch
ange
pr
oble
m,t
hen
the
prob
lem
invo
lves
a p
erce
nt o
f (i
ncre
ase/
decr
ease
).
2.If
you
use
(ne
w a
mou
nt)
— (
orig
inal
am
ount
) to
fin
d th
e ch
ange
for
a p
erce
nt o
f ch
ange
pr
oble
m,t
hen
the
prob
lem
invo
lves
a p
erce
nt o
f (i
ncre
ase/
decr
ease
).
Com
ple
te t
he
char
t.
Ori
gina
lN
ew
Per
cent
Incr
ease
or
Am
ount
Am
ount
Per
cent
Pro
port
ion
Per
cent
Dec
reas
e?
3.10
13!
incr
ease
4.10
7!
decr
ease
5.50
42!
decr
ease
6.50
58!
incr
ease
7.W
hen
you
find
a d
isco
unt
pric
e,do
you
add
to
or s
ubtr
act
from
the
ori
gina
l pri
ce?
subt
ract
Hel
ping
You
Rem
embe
r
8.If
you
rem
embe
r on
ly t
wo
thin
gs a
bout
the
rat
io u
sed
for
find
ing
perc
ent
of c
hang
e,w
hat
shou
ld t
hey
be?
Sub
trac
t th
e pr
ices
, the
n di
vide
by
the
orig
inal
num
ber.
r"
8 "→ →
chan
ge"
r"
8 "→ →
chan
ge"
r"
3 "→ →
chan
ge"
r"
3 "→ →
chan
ge"
incr
ease
decr
ease
©G
lenc
oe/M
cGra
w-H
ill17
8G
lenc
oe A
lgeb
ra 1
Usi
ng P
erce
ntU
se w
hat
you
hav
e le
arn
ed a
bou
t p
erce
nt
to s
olve
eac
h p
robl
em.
A T
V m
ovie
had
a “
rati
ng”
of 1
5 an
d a
25 “
shar
e.”T
he r
atin
g is
the
per
cent
age
of t
he n
atio
n’s
tota
l TV
hou
seho
lds
that
wer
e tu
ned
in t
o th
is s
how
.The
sha
reis
the
per
cent
age
of h
omes
wit
h T
Vs
turn
ed o
n th
at w
ere
tune
d to
the
mov
ie.
How
man
y T
V h
ouse
hold
s ha
d th
eir
TV
s tu
rned
off
at
this
tim
e?To
fin
d ou
t,le
t T
!th
e nu
mbe
r of
TV
hou
seho
lds
and
x!
the
num
ber
of T
V h
ouse
hold
s w
ith
the
TV
off.
The
n T
"x
!th
e nu
mbe
r of
TV
hou
seho
lds
wit
h th
e T
V o
n.Si
nce
0.15
Tan
d 0.
25(T
"x)
bot
h re
pres
ent
the
num
ber
of h
ouse
hold
s tu
ned
to t
he m
ovie
, 0.15
T!
0.25
(T"
x)0.
15T
!0.
25T
"0.
25x.
Solv
e fo
r x.
0.25
x!
0.10
Tx
!!
0.40
T
Fort
y pe
rcen
t of
the
TV
hou
seho
lds
had
thei
r T
Vs
off w
hen
the
mov
ie w
as a
ired
.
An
swer
eac
h q
ues
tion
.
1.D
urin
g th
at s
ame
wee
k,a
spor
ts b
road
cast
had
a r
atin
g of
22.
1 an
d a
43 s
hare
.Sh
ow t
hat
the
perc
ent
of T
V h
ouse
hold
s w
ith
thei
r T
Vs
off w
as a
bout
48.
6%.
0.22
1T!
0.43
T#
0.43
xx
! !0.
486T
2.F
ind
the
perc
ent
of T
V h
ouse
hold
s w
ith
thei
r T
Vs
turn
ed o
ff d
urin
g a
show
w
ith
a ra
ting
of
18.9
and
a 2
9 sh
are.
34.8
%
3.Sh
ow t
hat
if T
is t
he n
umbe
r of
TV
hou
seho
lds,
r is
the
rat
ing,
and
s is
the
shar
e,th
en t
he n
umbe
r of
TV
hou
seho
lds
wit
h th
e T
V o
ff is
.
Sol
ve r
T!
s(T
#x)
for
x.
4.If
the
fra
ctio
n of
TV
hou
seho
lds
wit
h no
TV
on
is
then
sho
w t
hat
the
frac
tion
of T
V h
ouse
hold
s w
ith
TV
s on
is
.
5.F
ind
the
perc
ent
of T
V h
ouse
hold
s w
ith
TV
s on
dur
ing
the
mos
t w
atch
ed
seri
al p
rogr
am in
his
tory
:the
last
epi
sode
of
M*A
*S*H
,whi
ch h
ad a
60.
3 ra
ting
and
a 7
7 sh
are.
!78
.3%
6.A
loca
l sta
tion
now
has
a 2
sha
re.E
ach
shar
e is
wor
th $
50,0
00 in
adv
erti
sing
re
venu
e pe
r m
onth
.The
sta
tion
is t
hink
ing
of g
oing
com
mer
cial
free
for
the
thre
e m
onth
s of
sum
mer
to
gain
mor
e lis
tene
rs.W
hat
wou
ld it
s ne
w s
hare
ha
ve t
o be
for
the
last
4 m
onth
s of
the
yea
r to
mak
e m
ore
mon
ey fo
r th
e ye
ar
than
it w
ould
hav
e m
ade
had
it n
ot g
one
com
mer
cial
free
?gr
eate
r th
an 3
.5
60.3
"
r # s
s –
r#
s
(s"
r)T
#s
0.22
1T#
0.43
T"
"
0.10
T# 0.
25
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-7
3-7
1 #
!r "
s#
r"
Answers (Lesson 3-7)
© Glencoe/McGraw-Hill A23 Glencoe Algebra 1
An
swer
s
Stu
dy
Gu
ide
an
d I
nte
rven
tion
Sol
ving
Equ
atio
ns a
nd F
orm
ulas
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-8
3-8
©G
lenc
oe/M
cGra
w-H
ill17
9G
lenc
oe A
lgeb
ra 1
Lesson 3-8
Solv
e fo
r V
aria
ble
sSo
met
imes
you
may
wan
t to
sol
ve a
n eq
uati
on s
uch
as V
"!w
hfo
ron
e of
its
vari
able
s.Fo
r ex
ampl
e,if
you
kno
w t
he v
alue
s of
V,w
,and
h,t
hen
the
equa
tion
!"
is m
ore
usef
ul f
or f
indi
ng t
he v
alue
of !
.If
an e
quat
ion
that
con
tain
s m
ore
than
one
vari
able
is t
o be
sol
ved
for
a sp
ecif
ic v
aria
ble,
use
the
prop
erti
es o
f eq
ualit
y to
isol
ate
the
spec
ifie
d va
riab
le o
n on
e si
de o
f th
e eq
uati
on.
V % wh
Sol
ve 2
x!
4y"
8 fo
r y.
2x#
4y"
82x
#4y
#2x
"8
#2x
#4y
"8
#2x
"
y"
or
The
val
ue o
f yis
.
2x#
8%
4
2x#
8%
48
#2x
%#
4
8 #
2x%
#4
#4y
% #4
Sol
ve 3
m!
n"
km
!8
for
m.
3m#
n"
km#
83m
#n
#km
"km
#8
#km
3m#
n#
km"
#8
3m#
n#
km'
n"
#8
'n
3m#
km"
#8
'n
m(3
#k)
"#
8 '
n
"
m"
,or
The
val
ue o
f mis
.S
ince
div
isio
n by
0 is
unde
fine
d,3
#k
(0,
or k
(3.
n#
8% 3
#k
n#
8% 3
#k
#8
'n
%3
#k
#8
'n
%3
#k
m(3
#k)
%%
3 #
k
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Sol
ve e
ach
equ
atio
n o
r fo
rmu
la f
or t
he
vari
able
sp
ecif
ied
.
1.ax
#b
"c
for
x2.
15x
'1
"y
for
x3.
(x'
f) '
2 "
jfor
x
x"
,a*
0x
"x
"j!
2 !
f
4.xy
'z
"9
for
y5.
x(4
#k)
"p
for
k6.
7x'
3y"
mfo
r y
y"
,x*
0k
"4
!,x
*0
y"
7.4(
c'
3) "
tfo
r c
8.2x
'b
"c
for
x9.
x(1
'y)
"z
for
x
c"
!3
x"
x"
,y*
!1
10.1
6z'
4x"
yfo
r x
11.d
"rt
for
r12
.A"
for
h
x"
r"
,t*
0h
",a
*!
b
13.C
"(F
#32
) fo
r F
14.P
"2!
'2w
for
w15
.A"
!wfo
r !
F"
C#
32w
"!
",w
*0
A % wP
!2!
%2
9 % 5
5 % 9
2A% a
#b
d % ty
!16
z%
4
h(a
'b)
%% 2z
% 1 #
yc
!b
%2
t % 4
m!
7x%
3p % x
9 !
z%
x
y!
1%
15c
#b
%a
©G
lenc
oe/M
cGra
w-H
ill18
0G
lenc
oe A
lgeb
ra 1
Use
Fo
rmu
las
Man
y re
al-w
orld
pro
blem
s re
quir
e th
e us
e of
for
mul
as.S
omet
imes
sol
ving
a fo
rmul
a fo
r a
spec
ifie
d va
riab
le w
ill h
elp
solv
e th
e pr
oble
m.
Th
e fo
rmu
la C
"$
dre
pre
sen
ts t
he
circ
um
fere
nce
of
a ci
rcle
,or
the
dis
tan
ce a
rou
nd
th
e ci
rcle
,wh
ere
dis
th
e d
iam
eter
.If
an a
irp
lan
e co
uld
fly
aro
un
dE
arth
at
the
equ
ator
wit
hou
t st
opp
ing,
it w
ould
hav
e tr
avel
ed a
bou
t 24
,900
mil
es.
Fin
d t
he
dia
met
er o
f E
arth
.
C"
&d
Giv
en fo
rmul
a
d"
Sol
ve fo
r d.
d"
Use
&"
3.14
.
d!
7930
Sim
plify
.
The
dia
met
er o
f E
arth
is a
bout
793
0 m
iles.
1.G
EOM
ETRY
The
vol
ume
of a
cyl
inde
r V
is g
iven
by
the
form
ula
V"
&r2
h,w
here
ris
the
radi
us a
nd h
is t
he h
eigh
t.
a.So
lve
the
form
ula
for
h.h
"
b.F
ind
the
heig
ht o
f a
cylin
der
wit
h vo
lum
e 25
00&
feet
and
rad
ius
10 f
eet.
25 f
t
2.W
ATE
R P
RES
SUR
ET
he w
ater
pre
ssur
e on
a s
ubm
erge
d ob
ject
is g
iven
by
P"
64d,
whe
re P
is t
he p
ress
ure
in p
ound
s pe
r sq
uare
foot
,and
dis
the
dep
th o
f the
obj
ect
in fe
et.
a.So
lve
the
form
ula
for
d.d
"
b.F
ind
the
dept
h of
a s
ubm
erge
d ob
ject
if t
he p
ress
ure
is 6
72 p
ound
s pe
r sq
uare
foot
.10
.5 ft
3.G
RA
PHS
The
equ
atio
n of
a li
ne c
onta
inin
g th
e po
ints
(a,0
) an
d (0
,b)
is g
iven
by
the
form
ula
'"
1.
a.So
lve
the
equa
tion
for
y.
y"
b!1
!"
b.Su
ppos
e th
e lin
e co
ntai
ns t
he p
oint
s (4
,0),
and
(0,#
2).I
f x"
3,fi
nd y
.!
4.G
EOM
ETRY
The
sur
face
are
a of
a r
ecta
ngul
ar s
olid
is g
iven
by
the
form
ula
S"
2!w
'2!
h'
2wh,
whe
re !
"le
ngth
,w"
wid
th,a
nd h
"he
ight
.
a.So
lve
the
form
ula
for
h.h
"
b.T
he s
urfa
ce a
rea
of a
rec
tang
ular
sol
id w
ith
leng
th 6
cen
tim
eter
s an
d w
idth
3
cent
imet
ers
is 7
2 sq
uare
cen
tim
eter
s.F
ind
the
heig
ht.
2 cm
S!
2!w
%%
2!#
2w
1 % 2
x % a
y % bx % a
P % 64V % $r2
24,9
00%
3.14
C % &
Stu
dy
Gu
ide
and I
nte
rven
tion
(c
onti
nued
)
Sol
ving
Equ
atio
ns a
nd F
orm
ulas
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-8
3-8
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 3-8)
©G
lencoe/McG
raw-H
illA
24G
lencoe Algebra 1
Skills PracticeSolving Equations and Formulas
NAME ______________________________________________ DATE ____________ PERIOD _____
3-83-8
© Glencoe/McGraw-Hill 181 Glencoe Algebra 1
Less
on
3-8
Solve each equation or formula for the variable specified.
1. 7t " x, for t t " 2. e " wp, for p p "
3. q # r " r, for r r " 4. 4m # n " m, for m m "
5. 7a # b " 15a, for a a " ! 6. #5c ' d " 2c, for c c "
7. x # 2y " 1, for y y " 8. m ' 3n " 1, for n n "
9. 7f ' g " 5, for f f " 10. ax # c " b, for x x "
11. rt # 2n " y, for t t " 12. bc ' 3g " 2k, for c c "
13. kn ' 4f " 9v, for n n " 14. 8c ' 6j " 5p, for c c "
15. " d, for x x " c # 2d 16. " d, for c c " x ! 2d
17. " q, for p p " 5q ! 9 18. " a, for b b " 7a # 4z
Write an equation and solve for the variable specified.
19. Five more than a number g is six less than twice a number h. Solve for g.
g # 5 " 2h ! 6; g " 2h ! 11
20. One fourth of a number q is three more than three times a number w. Solve for q.
q " 3w # 3; q " 12w # 12
21. Eight less than a number s is three more than four times a number t. Solve for s.
s ! 8 " 4t # 3; s " 4t # 11
1%4
b # 4z%7
p ' 9%5
x # c%2
x # c%2
5p ! 6j%8
9v ! 4f%k
2k ! 3g%b
2n # y%r
b # c%a
5 ! g%7
1 ! m%3
x ! 1%2
d%7
b%8
n%3
q%2
e%w
x%7
© Glencoe/McGraw-Hill 182 Glencoe Algebra 1
Solve each equation or formula for the variable specified.
1. d " rt, for r r " 2. 6w # y " 2z, for w w "
3. mx ' 4y " 3c, for x x " 4. 9s # 5g " #4u, for s s "
5. ab ' 3c " 2d, for b b " 6. 2p " kx # q, for x x "
7. m ' a " a ' c, for m m " c 8. h ' g " d, for h h " (d ! g)
9. y ' v " s, for y y " (s ! v) 10. a # q " k, for a a " (k # q)
11. " h, for x x " 12. " c, for b b "
13. 2w # y " 7w # 2, for w w " 14. 3! ' y " 5 ' 5!, for ! ! "
Write an equation and solve for the variable specified.
15. Three times a number s plus 4 times a number y is 1 more than 6 times the number s.Solve for s.3s # 4y " 6s # 1; s "
16. Five times a number k minus 9 is two thirds of a number j. Solve for j.
5k ! 9 " j; j " (5k ! 9)
ELECTRICITY For Exercises 17 and 18, use the following information.
The formula for Ohm’s Law is E " IR, where E represents voltage measured in volts,I represents current measured in amperes, and R represents resistance measured in ohms.
17. Solve the formula for R. R "
18. Suppose a current of 0.25 ampere flows through a resistor connected to a 12-volt battery.What is the resistance in the circuit? 48 ohms
MOTION For Exercises 19 and 20, use the following information.
In uniform circular motion, the speed v of a point on the edge of a spinning disk is v " r,
where r is the radius of the disk and T is the time it takes the point to travel once aroundthe circle.
19. Solve the formula for r. r "
20. Suppose a merry-go-round is spinning once every 3 seconds. If a point on the outsideedge has a speed of 12.56 feet per second, what is the radius of the merry-go-round? (Use 3.14 for &.) 6 ft
Tv%2$
2&%T
E%I
3%2
2%3
4y ! 1%3
y ! 5%2
2 ! y%5
2c # 4%3
3b # 4%2
5h ! 9%r
rx ' 9%5
4%3
3%4
3%2
2%3
5%2
2%5
3%2
2%3
2p # q%k
2d ! 3c%a
!4u #5g%%9
3c ! 4y%m
2z # y%6
d%t
Practice (Average)
Solving Equations and Formulas
NAME ______________________________________________ DATE ____________ PERIOD _____
3-83-8
Answ
ers(Lesson 3-8)
© Glencoe/McGraw-Hill A25 Glencoe Algebra 1
Ans
wer
s
Rea
din
g t
o L
earn
Math
emati
csS
olvi
ng E
quat
ions
and
For
mul
as
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-8
3-8
©G
lenc
oe/M
cGra
w-H
ill18
3G
lenc
oe A
lgeb
ra 1
Lesson 3-8
Pre-
Act
ivit
yH
ow a
re e
quat
ion
s u
sed
to
des
ign
rol
ler
coas
ters
?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 3-
8 at
the
top
of
page
166
in y
our
text
book
.
The
equ
atio
n g(
195
!h)
"v2
cont
ains
sev
eral
var
iabl
es.W
hat
num
ber
valu
es d
o yo
u kn
ow f
or t
hese
var
iabl
es in
thi
s si
tuat
ion?
32 f
org
and
49 f
orv
Read
ing
the
Less
on
1.Su
ppos
e yo
u ha
ve a
n eq
uati
on w
ith
seve
ral v
aria
bles
.You
wan
t to
sol
ve f
or a
par
ticu
lar
vari
able
.How
doe
s th
e pr
oced
ure
com
pare
wit
h th
at f
or s
olvi
ng a
n eq
uati
on w
ith
just
one
vari
able
? H
ow d
oes
the
solu
tion
com
pare
wit
h th
e so
luti
on f
or a
n eq
uati
on w
ith
one
vari
able
?
Sam
ple
answ
er:
The
proc
edur
e is
bas
ical
ly t
he s
ame.
You
use
pro
pert
ies
of o
pera
tions
and
equ
ality
to
isol
ate
the
vari
able
in w
hich
you
are
inte
rest
ed. T
he s
olut
ion
will
pro
babl
y co
ntai
n va
riab
les
inst
ead
of ju
st a
num
ber.
2.D
escr
ibe
wha
t di
men
sion
al a
naly
sis
invo
lves
.
Sam
ple
answ
er: Y
ou u
se t
he u
nits
alo
ng w
ith n
umbe
r va
lues
as
you
doca
lcul
atio
ns. Y
ou t
reat
the
uni
ts p
rett
y m
uch
the
sam
e w
ay y
ou w
ould
vari
able
s. F
or e
xam
ple,
you
can
div
ide
them
and
use
exp
onen
ts w
ithth
em.
3.W
hat
do y
ou h
ave
to b
e ca
refu
l abo
ut w
hen
you
use
vari
able
s in
den
omin
ator
s of
frac
tion
s?
You
have
to
be s
ure
that
you
do
not
use
valu
es t
hat
wou
ld m
ake
the
deno
min
ator
0.
Hel
ping
You
Rem
embe
r
4.W
hen
you
give
the
dim
ensi
ons
of a
rec
tang
le,y
ou h
ave
to t
ell h
ow m
any
unit
s lo
ng it
isan
d ho
w m
any
unit
s w
ide
it is
.How
can
thi
s he
lp y
ou r
emem
ber
wha
t di
men
sion
alan
alys
is in
volv
es.
Sam
ple
answ
er:
Kee
p th
e w
ords
dim
ensi
onan
d un
itin
min
d. In
dim
ensi
onal
ana
lysi
s, y
ou in
clud
e un
its f
or d
imen
sion
s in
cal
cula
tions
.
1 # 2
©G
lenc
oe/M
cGra
w-H
ill18
4G
lenc
oe A
lgeb
ra 1
Dr.
Ber
nard
o H
ouss
ay
Eve
n th
ough
res
earc
hers
hav
e be
en s
tudy
ing
the
dise
ase
diab
etes
mel
litu
sfo
r hu
ndre
ds o
f ye
ars,
scie
ntis
ts h
ave
only
rec
entl
y di
scov
ered
the
caus
e of
the
dis
ease
and
dev
elop
ed m
etho
ds f
or r
educ
ing
its
seve
rity
.Dr.
Ber
nard
o H
ouss
ay,a
n A
rgen
tine
phy
siol
ogis
t,w
as o
ne o
fth
e pi
onee
rs o
f th
is m
ore
mod
ern
rese
arch
.He
stud
ied
the
rela
tion
ship
betw
een
diab
etes
and
the
pit
uita
ry g
land
,and
in 1
947
beca
me
the
firs
tL
atin
Am
eric
an t
o w
in t
he N
obel
Pri
ze in
Med
icin
e an
d P
hysi
olog
y.
Tho
ugh
ther
e is
no
cure
for
diab
etes
,spe
cific
die
ts a
nd e
xerc
ise
can
help
peop
le c
ontr
ol t
he d
isea
se.T
he A
mer
ican
Dia
bete
s A
ssoc
iati
on (A
DA
)ha
s he
lped
est
ablis
h fle
xibl
e di
etar
y gu
idel
ines
for
cons
umer
s to
follo
w.
The
se g
uide
lines
incl
ude
som
e of
the
follo
win
g ge
nera
l nut
riti
on r
ules
.
•Fa
t in
take
sho
uld
be e
qual
to
or le
ss t
han
30%
of
daily
cal
orie
s.
•Sa
tura
ted
fat
inta
ke s
houl
d be
equ
al t
o or
less
tha
n 10
% o
f da
ilyca
lori
es.
•P
rote
in s
houl
d be
lim
ited
to
10%
to
20%
of
daily
cal
orie
s.Pe
rson
ssh
owin
g th
e in
itia
l sig
ns o
f di
abet
es-i
nduc
ed k
idne
y di
seas
e sh
ould
limit
pro
tein
to
10%
of
daily
cal
orie
s.
•C
hole
ster
ol in
take
sho
uld
be 3
00 m
illig
ram
s or
less
dai
ly.
Ref
er t
o th
e in
form
atio
n a
bove
for
Exe
rcis
es 1
–4.
1.R
ober
t co
nsum
ed 2
100
calo
ries
on
Tue
sday
.His
fat
inta
ke t
otal
ed70
gra
ms,
and
of t
hat
70 g
ram
s,14
wer
e sa
tura
ted.
a.W
hat
perc
enta
ge o
f hi
s ca
lori
e co
nsum
ptio
n w
as f
at,a
nd w
hat
perc
enta
ge o
f th
at f
at w
as s
atur
ated
? (T
o fi
nd t
he p
erce
ntag
e of
calo
ries
fro
m f
at,m
ulti
ply
the
num
ber
of f
at g
ram
s by
9 b
efor
edi
vidi
ng b
y th
e nu
mbe
r of
cal
orie
s.) 3
0%;
20%
b.D
id R
ober
t st
ay w
ithi
n th
e re
com
men
ded
allo
wan
ce o
f fa
ts?
yes
2.A
nna'
s ch
oles
tero
l int
ake
was
330
mill
igra
ms
on S
unda
y.B
y w
hat
perc
enta
ge d
oes
she
need
to
redu
ce h
er c
hole
ster
ol c
onsu
mpt
ion
tore
mai
n w
ithi
n th
e gu
idel
ines
? 10
%
3.W
hat
num
ber
of f
at g
ram
s is
30%
of
240
calo
ries
? 8
4.Sh
aron
fol
low
s a
diet
tha
t pr
ovid
es a
bout
50
gram
s of
pro
tein
eac
hda
y.Sh
aron
's d
octo
r ha
s ju
st t
old
her
to r
educ
e he
r da
ily p
rote
inin
take
by
30%
.Abo
ut h
ow m
uch
prot
ein
will
be
in h
er r
educ
edpr
otei
n di
et?
35 g
ram
s
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-8
3-8
Answers (Lesson 3-8)
©G
lencoe/McG
raw-H
illA
26G
lencoe Algebra 1
Study Guide and InterventionWeighted Averages
NAME ______________________________________________ DATE ____________ PERIOD _____
3-93-9
© Glencoe/McGraw-Hill 185 Glencoe Algebra 1
Less
on
3-9
Mixture Problems
Weighted AverageThe weighted average M of a set of data is the sum of the product of each number in the set and its weight divided by the sum of all the weights.
Mixture Problems are problems where two or more parts are combined into a whole. Theyinvolve weighted averages. In a mixture problem, the weight is usually a price or a percentof something.
Delectable Cookie Company sells chocolate chip cookies for $6.95per pound and white chocolate cookies for $5.95 per pound. How many pounds ofchocolate chip cookies should be mixed with 4 pounds of white chocolate cookiesto obtain a mixture that sells for $6.75 per pound.
Let w " the number of pounds of chocolate chip cookies
Number of Pounds Price per Pound Total Price
Chocolate Chip w 6.95 6.95w
White Chocolate 4 5.95 4(5.95)
Mixture w ' 4 6.75 6.75(w ' 4)
Equation: 6.95w ' 4(5.95) " 6.75(w ' 4)Solve the equation.
6.95w ' 4(5.95) " 6.75(w ' 4) Original equation6.95w ' 23.80 " 6.75w ' 27 Simplify.
6.95w ' 23.80 # 6.75w " 6.75w ' 27 # 6.75w Subtract 6.75w from each side.0.2w ' 23.80 " 27 Simplify.
0.2w ' 23.80 # 23.80 " 27 # 23.80 Subtract 23.80 from each side.0.2w " 3.2 Simplify.
w " 16 Simplify.
16 pounds of chocolate chip cookies should be mixed with 4 pounds of white chocolate cookies.
1. SOLUTIONS How many grams of sugar must be added to 60 grams of a solution that is32% sugar to obtain a solution that is 50% sugar? 21.6 g
2. NUTS The Quik Mart has two kinds of nuts. Pecans sell for $1.55 per pound andwalnuts sell for $1.95 per pound. How many pounds of walnuts must be added to 15pounds of pecans to make a mixture that sells for $1.75 per pound? 15 lb
3. INVESTMENTS Alice Gleason invested a portion of $32,000 at 9% interest and thebalance at 11% interest. How much did she invest at each rate if her total income fromboth investments was $3,200. $16,000 at 9% and $16,000 at 11%
4. MILK Whole milk is 4% butterfat. How much skim milk with 0% butterfat should beadded to 32 ounces of whole milk to obtain a mixture that is 2.5% butterfat? 19.2 oz
ExampleExample
ExercisesExercises
© Glencoe/McGraw-Hill 186 Glencoe Algebra 1
Uniform Motion Problems Motion problems are another application of weightedaverages. Uniform motion problems are problems where an object moves at a certainspeed, or rate. Use the formula d " rt to solve these problems, where d is the distance, r isthe rate, and t is the time.
Bill Gutierrez drove at a speed of 65 miles per hour on anexpressway for 2 hours. He then drove for 1.5 hours at a speed of 45 miles perhour on a state highway. What was his average speed?
M " Definition of weighted average
! 56.4 Simplify.
Bill drove at an average speed of about 56.4 miles per hour.
1. TRAVEL Mr. Anders and Ms. Rich each drove home from a business meeting. Mr. Anderstraveled east at 100 kilometers per hour and Ms. Rich traveled west at 80 kilometers perhours. In how many hours were they 100 kilometers apart. h
2. AIRPLANES An airplane flies 750 miles due west in 1 hours and 750 miles due south
in 2 hours. What is the average speed of the airplane? about 429 mph
3. TRACK Sprinter A runs 100 meters in 15 seconds, while sprinter B starts 1.5 secondslater and runs 100 meters in 14 seconds. If each of them runs at a constant rate, who isfurther in 10 seconds after the start of the race? Explain.
Sprinter A; since sprinter A runs 100 m in 15 s, this sprinter runs at a
rate of m/s. In 10 seconds, sprinter A will have run (10) " 66.7 m.
Sprinter B’s rate is . In 10 seconds, with the delayed start, sprinter B
has run (10 ! 1.5) " 60.7 m.
4. TRAINS An express train travels 90 kilometers per hour from Smallville to Megatown.A local train takes 2.5 hours longer to travel the same distance at 50 kilometers perhour. How far apart are Smallville and Megatown? 281.25 km
5. CYCLING Two cyclists begin traveling in the same direction on the same bike path. Onetravels at 15 miles per hour, and the other travels at 12 miles per hour. When will thecyclists be 10 miles apart? 3 h
6. TRAINS Two trains leave Chicago, one traveling east at 30 miles per hour and onetraveling west at 40 miles per hour. When will the trains be 210 miles apart? 3 h
1%3
100%14
100%14
100%15
100%15
1%2
5%9
65 ) 2 ' 45 ) 1.5%%2 ' 1.5
Study Guide and Intervention (continued)
Weighted Averages
NAME ______________________________________________ DATE ____________ PERIOD _____
3-93-9
ExampleExample
ExercisesExercises
Answ
ers(Lesson 3-9)
©G
lencoe/McG
raw-H
illA
27G
lencoe Algebra 1
Answers
Skills PracticeWeighted Averages
NAME ______________________________________________ DATE ____________ PERIOD _____
3-93-9
© Glencoe/McGraw-Hill 187 Glencoe Algebra 1
Less
on
3-9
SEASONING For Exercises 1–4, use the following information.
A health food store sells seasoning blends in bulk. One blend contains 20% basil. Sheilawants to add pure basil to some 20% blend to make 16 ounces of her own 30% blend. Let brepresent the amount of basil Sheila should add to the 20% blend.
1. Complete the table representing the problem.
Ounces Amount of Basil
20% Basil Blend 16 ! b 0.20(16 ! b)
100% Basil b 1.00b
30% Basil Blend 16 0.30(16)
2. Write an equation to represent the problem. 0.20(16 ! b) # 1.00b " 0.30(16)
3. How many ounces of basil should Sheila use to make the 30% blend? 2 oz
4. How many ounces of the 20% blend should she use? 14 oz
HIKING For Exercises 5–7, use the following information.
At 7:00 A.M., two groups of hikers begin 21 miles apart and head toward each other. The firstgroup, hiking at an average rate of 1.5 miles per hour, carries tents, sleeping bags, andcooking equipment. The second group, hiking at an average rate of 2 miles per hour, carriesfood and water. Let t represent the hiking time.
5. Copy and complete the table representing the problem.
r t d " rt
First group of hikers 1.5 t 1.5t
Second group of hikers 2 t 2t
6. Write an equation using t that describes the distances traveled. 1.5t # 2t " 21
7. How long will it be until the two groups of hikers meet? 6 h
SALES For Exercises 8 and 9, use the following information.
Sergio sells a mixture of Virginia peanuts and Spanish peanuts for $3.40 per pound. Tomake the mixture, he uses Virginia peanuts that cost $3.50 per pound and Spanish peanutsthat cost $3.00 per pound. He mixes 10 pounds at a time.
8. How many pounds of Virginia peanuts does Sergio use? 8 lb
9. How many pounds of Spanish peanuts does Sergio use? 2 lb
© Glencoe/McGraw-Hill 188 Glencoe Algebra 1
GRASS SEED For Exercises 1–4, use the following information.
A nursery sells Kentucky Blue Grass seed for $5.75 per pound and Tall Fescue seed for$4.50 per pound. The nursery sells a mixture of the two kinds of seed for $5.25 per pound.Let k represent the amount of Kentucky Blue Grass seed the nursery uses in 5 pounds ofthe mixture.
1. Complete the table representing the problem.
Number of Pounds Price per Pound Cost
Kentucky Blue Grass k $5.75 5.75k
Tall Fescue 5 ! k $4.50 4.50(5 ! k)
Mixture 5 $5.25 5.25(5)
2. Write an equation to represent the problem. 5.75k # 4.50(5 ! k) " 5.25(5)
3. How much Kentucky Blue Grass does the nursery use in 5 pounds of the mixture? 3 lb
4. How much Tall Fescue does the nursery use in 5 pounds of the mixture? 2 lb
TRAVEL For Exercises 5–7, use the following information.
Two commuter trains carry passengers between two cities, one traveling east, and the otherwest, on different tracks. Their respective stations are 150 miles apart. Both trains leave atthe same time, one traveling at an average speed of 55 miles per hour and the other at anaverage speed of 65 miles per hour. Let t represent the time until the trains pass each other.
5. Copy and complete the table representing the problem.
r t d " rt
First Train 55 t 55t
Second Train 65 t 65t
6. Write an equation using t that describes the distances traveled. 55t # 65t " 150
7. How long after departing will the trains pass each other? 1.25 h
8. TRAVEL Two trains leave Raleigh at the same time, one traveling north, and the othersouth. The first train travels at 50 miles per hour and the second at 60 miles per hour.In how many hours will the trains be 275 miles apart? 2.5 h
9. JUICE A pineapple drink contains 15% pineapple juice. How much pure pineapple juiceshould be added to 8 quarts of the drink to obtain a mixture containing 50% pineapplejuice? 5.6 qt
Practice (Average)
Weighted Averages
NAME ______________________________________________ DATE ____________ PERIOD _____
3-93-9
Answ
ers(Lesson 3-9)
© Glencoe/McGraw-Hill A28 Glencoe Algebra 1
Rea
din
g t
o L
earn
Math
emati
csW
eigh
ted
Ave
rage
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
3-9
3-9
©G
lenc
oe/M
cGra
w-H
ill18
9G
lenc
oe A
lgeb
ra 1
Lesson 3-9
Pre-
Act
ivit
yH
ow a
re s
core
s ca
lcu
late
d i
n a
fig
ure
sk
atin
g co
mp
etit
ion
?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 3-
9 at
the
top
of
page
171
in y
our
text
book
.
Why
is t
he s
um o
f Il
ia K
ulik
’s s
core
s di
vide
d by
3?
Her
fir
st s
core
is c
ount
ed o
nce
and
her
seco
nd s
core
isco
unte
d tw
ice.
Rea
din
g t
he
Less
on
1.R
ead
the
defi
niti
on o
f wei
ghte
d av
erag
eon
pag
e 17
1 of
you
r te
xtbo
ok.W
hat
is m
eant
by
the
wei
ght
of a
num
ber
in a
set
of
data
?
the
num
ber
of t
imes
the
num
ber
occu
rs in
the
set
of
data
2.L
inda
’s q
uiz
scor
es in
sci
ence
are
90,
85,8
5,75
,85,
and
90.W
hat
is t
he w
eigh
t of
the
scor
e 85
?3
3.Su
ppos
e C
lint
driv
es a
t 50
mile
s pe
r ho
ur f
or 2
hou
rs.T
hen
he d
rive
s at
60
mile
s pe
rho
ur f
or 3
hou
rs.
a.W
rite
his
spe
ed f
or e
ach
hour
of
the
trip
.
Spe
ed50
5060
6060
Hou
r1
23
45
b.W
hat
is t
he w
eigh
t of
eac
h of
the
tw
o sp
eeds
?50
mph
:2;6
0 m
ph:3
Hel
pin
g Y
ou
Rem
emb
er
4.M
akin
g a
tabl
e ca
n be
hel
pful
in s
olvi
ng m
ixtu
re p
robl
ems.
In y
our
own
wor
ds,e
xpla
inho
w y
ou u
se a
tab
le t
o so
lve
mix
ture
pro
blem
s.
Com
plet
e ea
ch r
ow t
o w
rite
an
expr
essi
on in
the
last
col
umn
for
each
part
of
the
prob
lem
and
for
the
com
bina
tion,
then
wri
te a
n eq
uatio
nus
ing
thos
e ex
pres
sion
s fr
om t
he la
st c
olum
n.
©G
lenc
oe/M
cGra
w-H
ill19
0G
lenc
oe A
lgeb
ra 1
Dio
phan
tine
Equ
atio
nsT
he f
irst
gre
at a
lgeb
rais
t,D
ioph
antu
s of
Ale
xand
ria
(abo
ut A
.D.3
00),
devo
ted
muc
h of
his
wor
k to
the
sol
ving
of
inde
term
inat
e eq
uati
ons.
An
inde
term
inat
e eq
uati
on h
as m
ore
than
one
var
iabl
e an
d an
unlim
ited
num
ber
of s
olut
ions
.An
exam
ple
is x
'2y
"4.
Whe
n th
e co
effi
cien
ts o
f an
inde
term
inat
e eq
uati
on a
re in
tege
rs a
ndyo
u ar
e as
ked
to f
ind
solu
tion
s th
at m
ust
be in
tege
rs,t
he e
quat
ion
isca
lled
diop
hant
ine.
Such
equ
atio
ns c
an b
e qu
ite
diff
icul
t to
sol
ve,
ofte
n in
volv
ing
tria
l and
err
or—
and
som
e lu
ck!
Sol
ve e
ach
dio
ph
anti
ne
equ
atio
n b
y fi
nd
ing
at l
east
on
e p
air
of p
osit
ive
inte
gers
th
at m
akes
th
e eq
uat
ion
tru
e.S
ome
hin
ts a
re g
iven
to
hel
p y
ou.
1.2x
'5y
"32
a.F
irst
sol
ve t
he e
quat
ion
for
x.x
"16
!
b.W
hy m
ust
ybe
an
even
num
ber?
If y
is o
dd,t
hen
xw
on’t
be a
n in
tege
r.
c.F
ind
at le
ast
one
solu
tion
.A
ny o
f th
ese:
(11,
2),(
6,4)
,(1,
6)
2.5x
'2y
"42
a.F
irst
sol
ve t
he e
quat
ion
for
x.x
"
b.R
ewri
te y
our
answ
er in
the
for
m x
"8
'so
me
expr
essi
on.
x"
8 #
c.W
hy m
ust
(2 #
2y)
be a
mul
tipl
e of
5?
Oth
erw
ise,
xw
on’t
be a
n in
tege
r.
d.F
ind
at le
ast
one
solu
tion
.A
ny o
f th
ese:
(8,1
),(6
,6),
(4,1
1),(
2,16
)
3.2x
'7y
"29
4.7x
'5y
"11
8
(11,
1) o
r (4
,3)
Any
of
thes
e:(1
4,4)
,(9,
11),
(4,1
8)
5.8x
#13
y "
100
6.3x
'4y
"22
(19,
4),(
32,1
2) o
r an
y pa
ir
(6,1
) or
(2,
4)w
hen
y"
4nan
d n
is a
po
sitiv
e od
d nu
mbe
r
7.5x
#14
y"
118.
7x'
3y"
40
(5,1
),(1
9,6)
or
any
pair
(4
,4)
or (
1,11
)w
hen
y"
5m!
4 an
d m
is
a po
sitiv
e nu
mbe
r
2 !
2y%
5
42 !
2y%
5
5y % 2
En
rich
men
t
NA
ME
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ATE
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PE
RIO
D__
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3-9
3-9
Answers (Lesson 3-9)