Worksheet 3.1 Name: Messersmith – Beginning & Intermediate Algebra

9

8

0

Solve and check each equation.

1)

8 5p − =

2)

10 3n+ =

3)

4 t− = −

4) 2 1k =

5)

6 2y− =

6)

28 7 y− = −

7) 53x= −

8) 92a

=

9) 3 152

c =

10) 8 129

m− =

11) 4 7 1z 5+ =

12) 1 23

k 6− = −

Worksheet 3.1 Messersmith – Beginning & Intermediate Algebra

9

)

13) 8

6 0.25w= −

14) 9 4

7 11a a+ − + =

15) ( ) ( )3 2 5 4 2 7x x− + + = −

16) ( ) (9 6 1 2 9v v= + − −

Worksheet 3.2 Name: __________________________ Messersmith – Beginning & Intermediate Algebra Write an equation and solve.

1) Five more than a number is 12. Find the number.

2) Seven less than a number is −6. Find the number.

3) Nine less than a number is 11. Find the number.

4) Three-fourths of a number is 15. Find the number.

5) Twice the sum of a number and nine is 24. Find the number.

Worksheet 3.2 Messersmith – Beginning & Intermediate Algebra

6) Half of a number increased by seven is −2. Find the number.

7) A number decreased by two is eleven less than twice the number. Find the number.

8) Six less than a number is four more than one-third of the number. Find the number.

Worksheet 3.3 A Name: __________________________ Messersmith – Beginning & Intermediate Algebra Write an equation and solve.

1) Becky bought seven more packages of dried apples than packages of dried apricots. If she bought fifteen packages of these two fruits all together, how many of each did she buy?

2) In 2004, Illinois had one-third as many drive-in theaters as Pennsylvania. If the two states had a total of 48 drive-ins, how many did each state have? (Source: www.drive-ins.com)

3) According to the U.S. Geological Survey, the Mississippi River is 200 miles shorter than the Missouri River. Together, they cover a total of 4,880 miles. Find the lengths of each river. (Source: http://ga.water.usgs.gov)

Worksheet 3.3 A Messersmith – Beginning & Intermediate Algebra

4) A 42-cm piece of wire is to be cut into two pieces. One of the pieces is to be 10 cm longer than the other piece. Find the length of each piece of wire.

5) A 28-in. board is to be cut into two pieces so that one piece is one-third as long as the other piece. Find the length of each piece of board.

6) A furniture maker has 92 inches of decorative cord that she must cut into two pieces to put on a sofa. One piece must be 24 inches shorter than the other. Find the length of each piece.

Worksheet 3.3 B Name: __________________________ Messersmith – Beginning & Intermediate Algebra Write an equation and solve.

1) The sum of three consecutive integers is 72. What are the integers?

2) The sum of three consecutive odd integers is 63. What are the integers?

3) Find two consecutive even integers such that five times the smaller integer is ten more than three times the larger integer.

Worksheet 3.3 B Messersmith – Beginning & Intermediate Algebra

4) Luxurious Rental Cars charges $74.00 per day plus $.15 per mile to rent a convertible. If Isabella paid $95.60 for a one-day rental, how many miles did she drive?

5) Smith Builders paid $273.00 to rent a fork lift for several hours. The rental company charged them a flat fee of $147.00 plus $18.00 per hour. For how many hours did they have the fork lift?

Worksheet 3.4 A Name: Messersmith – Beginning & Intermediate Algebra

Solve.

1) A ladder that regularly sells for $105.00 is marked down 20%. a) How much money does Ely save if he buys it on sale? b) What is the sale price of the ladder?

2) If the number 80 is increased by 15% a) What is the amount of the increase?

b) What number results by increasing 80 by 15%?

3) A number increases from 250 to 305. Find the percent increase in the number.

Worksheet 3.4 A Messersmith – Beginning & Intermediate Algebra

Write an equation and solve.

4) An MP3 player is on sale for $162.00 after a 10% discount. What was the original price?

5) Terrell finds that if he takes a cruise in July it will cost $1200. This is 25% less than if he took the same cruise in December. What is the cost of taking the cruise in December?

6) After its expansion, a childcare facility could accommodate 54 children. This is 35% more children than it could serve the year before. How many children could the center hold before its expansion?

7) This year Penny’s salary is $29,120. This is 4% more than her salary last year. What did she earn last year?

Worksheet 3.4 B Name: __________________________ Messersmith – Beginning & Intermediate Algebra

For problems 1-4, answer the following two questions: a) How much interest is earned? b) How much money is in the account after one year?

1) $500 is invested for one year at 4% simple interest.

a) b)

2) $8000 is invested for one year at 5% simple interest.a) b)

3) x dollars is invested for one year at 3% simple interest.a) b)

4) $4000 is invested for one year at 5% simple interest and $600 is invested for one year at 6% simple interest. (Find the total interest and the total amount after one year.)

a) b)

Worksheet 3.4 B Messersmith – Beginning & Intermediate Algebra

Write an equation and solve.

5) Keisha has a total of $6000 to invest in two accounts for one year. One account pays 5% simple interest and the other pays 6% simple interest. How much should she invest in each account so that the total interest earned is $335?

6) Haroun has twice as much money invested in bonds paying 4% as he has in stocks paying 7%. How much money did he invest in each this year if he earned $750 from these investments?

7) Adrienne deposited some money in an account earning 4.5% simple interest and $3000 more than this in an account earning 6% simple interest. After one year, she earned a total of $390 in interest. How much did she deposit in each account?

Worksheet 3.5 Name: __________________________ Messersmith – Beginning & Intermediate Algebra Use a formula from geometry to write an equation and solve.

1) The volume of a rectangular box is 2160 in3. It is 10 inches wide and 18 inches long. What is the height of the box?

Find the measure of each indicated angle.

2) A

xº

(6x-8)º (-2+5x/2)º

C B 3)

(4x-3)º (2x+3)º

Worksheet 3.5 Messersmith – Beginning & Intermediate Algebra Write an equation and solve.

4) Find the measure of the angle such that the sum of its complement and supplement is 6º more than nine times the angle.

5) Find the measure of an angle such that the sum of its supplement and four times its complement is 13º less than twice the angle.

Worksheet 3.6 A Name: __________________________ Messersmith – Beginning & Intermediate Algebra Solve each proportion.

1) 2812 16k = 2) 5 7 1

5 15a a− +=

Set up a proportion and solve.

3) If four small pizzas cost $21.00, find the cost of six small pizzas.

4) The dosage for a certain medication is 12

teaspoon for every 30 pounds of body weight. What is

the dosage for a person who weighs 105 pounds?

5) If six crackers contain 70 calories, how many crackers would contain 175 calories?

Worksheet 3.6 B Name: __________________________ Messersmith – Beginning & Intermediate Algebra

Problems Involving Money 1) How much money do you have (in cents and in dollars) if you have:

a) 7 nickels?

b) 8 dimes?

c) 4 quarters?

d) 39 pennies?

e) n nickels?

t) d dimes?

g) q quarters?

h) p pennies?

i) n nickels and q quarters? Define the unknown(s), write an equation, and solve. 2) Marcus has $4.25 in change consisting of four more dimes than quarters. Find the number of dimes and quarters.

Worksheet 3.6 B Messersmith – Beginning & Intermediate Algebra 3) A cashier has only five-dollar and twenty-dollar bills in her register. If the register contains 19 bills worth $215, how many five-dollar bills does she have? 4) Tickets for a high school play cost $6 for adults and $4 for students. If $1348 were collected from the sale of 257 tickets, how many of each type of ticket was sold? 5) Jessica paid $5.95 for some $0.20 and $0.35 stamps. The number of $0.35 stamps was one less than twice as many $0.20 stamps. How many of each type of stamp did she buy?

Worksheet 3.6 C Name: __________________________ Messersmith – Beginning & Intermediate Algebra

Mixture Problems

1) How much pure acid is in 300 ml of a 15% acid solution?

2) How much pure alcohol is in 2 liters of a 20% alcohol solution?

3) How much pure acid is in x ml of a 17% acid solution?

4) If 120 ml of a 10% acid solution is mixed with 200 ml of a 4% acid solution, how much pure acid is in the mixture?

Write an equation and solve.

5) A chemist plans to mix 40 ml of a 5% alcohol solution with some 11% alcohol solution to make a 7% solution. How much of the 11% solution should she mix with the 5% solution to obtain the 7% alcohol solution?

Worksheet 3.6 C Messersmith – Beginning & Intermediate Algebra

6) An alloy that is 40% silver is mixed with 100g of a 10% silver alloy. How much of the 40% alloy must be used to obtain an alloy that is 25% silver?

7) A pharmacist needs to make 50 cubic centimeters (cc) of a 0.06% steroid solution. How much of a 0.02% and a 0.08% solution should he use?

8) A snack shop sells a mix consisting of peanuts and pretzels. How many pounds of peanuts, which sell for $4.00 per pound, should be mixed with pretzels, which sell for $2.50 per pound, to get 15 pounds of a mix worth $3.50 per pound?

Worksheet 3.6 D Name: __________________________ Messersmith – Beginning & Intermediate Algebra Write an equation and solve.

1) A passenger train and a freight train leave a station at the same time traveling in opposite

directions. The passenger train travels at 40 mph while the speed of the freight train is 25 mph. After how long will they be 260 miles apart?

2) A truck and a car leave an intersection at the same time traveling in the same direction. The truck’s speed is 30 mph, and the speed of the car is 40 mph. How long will it take before they are 5 miles apart?

Worksheet 3.6 D Messersmith – Beginning & Intermediate Algebra

3) Minh leaves his house on his bike going 5 mph. One-half hour later his brother Tan leaves on his bike following the same route at 10 mph. How long will it take for Tan to catch Minh?

4) The towns of Compton and Madera are 236 miles apart. Alia leaves Compton on the highway toward Madera at 58 mph. Cheryl leaves Madera at the same time going toward Compton on the same road. Her speed is 60 mph. When will Alia and Cheryl pass each other on the highway?

5) A truck passes the Oneida highway exit at 2 pm going 55 mph. Fifteen minutes later a motorcycle, headed in the same direction, passes the same exit at 70 mph. At what time will the motorcycle pass the truck?

Worksheet 3.7 Name: Messersmith – Beginning & Intermediate Algebra Write each inequality in interval notation.

1)

3x ≥

2)

8c ≤

3)

1p < −

4)

5k >

5) 1 62

y− ≤ ≤

6) 0 t 9≤ <

Solve each inequality. Graph the solution set and write the answer in a) set notation and b) interval notation. 7)

3 8a + ≤

8) 2c < −6

0

9)

5 2k− ≤

10) 2 1 33

n + <

11) 7 1

0 3y− ≥

Worksheet 3.7 Messersmith – Beginning & Intermediate Algebra

1

12)

8 3 4p− ≤ +

13) ( ) ( )2 7 5 3 2 1m m m− + < + +

14)

1 7 1 13w− ≤ − ≤

15) 82 65

n− < + ≤ 4

16) 3 5 2 11d< − <

Worksheet 3.8 Name: Messersmith – Beginning & Intermediate Algebra

t

Solve each compound inequality. Graph the solution set and write the answer in interval notation. 1)

3 and 4x x≥ − ≤

2)

10 8 and 3 15t − > − <

3)

2 1 8 and 5 6c c+ > − − >

4) 1 5 7 and 10 32

r r+ ≥ − ≥ −

5) 16 1 and 03

m − ≤ − ≥

6) 2 or 1a a< − >

0≤

9

7)

6 18 or 4y y≥ +

8) 5 4 2 or 9h h− − > + >

9) 37 2 or 11 22

w w≤ − + ≥

v

10) 8 1 6 or 5 2 9v− < − > m