3.11 more expressions and equation goals: to set up and solve word problems

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3.11 More Expressions and Equation • Goals: To set up and solve word problems

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The second math test was worth half as many as the first write an expression for the total number of points on both tests Let the first test be f Let the second test be s f+s = total points (but we can not have 2 variables!!!) s =1/2 f (now we can substitute!) f+1/2f

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Page 1: 3.11 More Expressions and Equation Goals: To set up and solve word problems

3.11 More Expressions and Equation

• Goals: To set up and solve word problems

Page 2: 3.11 More Expressions and Equation Goals: To set up and solve word problems

Graphic Organizer for Word Problems

• Ratios (Comparison of Units)• Percents (is/of= %/100)• Compound (x + (x+1))• If there are expressions with more then 1

type of variable we want to try to use substitution to get only one variable

Page 3: 3.11 More Expressions and Equation Goals: To set up and solve word problems

The second math test was worth half as many as the first write an expression

for the total number of points on both tests

• Let the first test be f• Let the second test be s• f+s = total points • (but we can not have 2 variables!!!)• s =1/2 f (now we can substitute!)• f+1/2f

Page 4: 3.11 More Expressions and Equation Goals: To set up and solve word problems

If “n” is the first integer, write an algebraic expression for the “2nd consecutive integer.”

n + 1Write an algebraic expression for the “3rd consecutive integer.” n + 2Write an algebraic expression for the sum of three consecutive integers.

n + (n + 1) + (n + 2)

Page 5: 3.11 More Expressions and Equation Goals: To set up and solve word problems

Find three consecutive integers whose sum is 90.

Let n = first integer

n + (n + 1) + (n + 2)

= 903n + 3 = 90

3n = 87n = 29

29, 30, and 31

Page 6: 3.11 More Expressions and Equation Goals: To set up and solve word problems

Write an algebraic expression for the “2nd consecutive odd integer.”

n + 2Write an algebraic expression for the “3rd consecutive odd integer.” n + 4Write an algebraic expression for the sum of three consecutive odd integers.

n + (n + 2) + (n + 4)

Page 7: 3.11 More Expressions and Equation Goals: To set up and solve word problems

Find three consecutive even integers whose sum is 42.

Let n = first integer

n + (n + 2) + (n + 4)

= 423n + 6 = 42

3n = 36n = 12

12, 14, and 16

Page 8: 3.11 More Expressions and Equation Goals: To set up and solve word problems

The sum of an integer and three times the next consecutive integer is 51.What is the largest number?

Let n = first integer

n + 3(n + 1) = 514n + 3 = 51

4n = 48n = 12 13

Page 9: 3.11 More Expressions and Equation Goals: To set up and solve word problems

The perimeter of a rectangle is 150 cm. The length is 15 cm greater than the width. Find

the dimensions• P = 2L + 2W• P=150• 150 = 2L +2W• L=(W +15)• 150 = 2 (W +15) +2W• 150 = 2W + 30 +2W• 150= 4W +30• 120 =4W• W=30 cm• L=30 +15 = 45 cm

Page 10: 3.11 More Expressions and Equation Goals: To set up and solve word problems

Homework:

Page 160 (2-22) evenYou do not have to write the word problem

down but you do have to write down the:• data, • draw a picture or diagram, • set up the equation • show your work to solve the equation • put the units on your answer

Page 11: 3.11 More Expressions and Equation Goals: To set up and solve word problems

Earn your P.s. D. (Problem Solving Degree)

• You are the “interns” and are trying to earn your Ps. D. ( Doctor of Problem Solving Degree)

• Diagnose a word problem as a doctor would a patient

• The vocabulary is the “Symptoms” that determine how we “Operate” to determine the correct answer.

• A “Final Check-Up” ensures the operation was successful.