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CHAPTER TEST A

Direct and Inverse Proportion5

Concepts and Skills (Questions 1 to 6: 6 � 1 point � 6 points, Questions 7 and 8: 2 � 2 points � 4 points)

Tell whether each table, graph, or equation represents a direct proportion, an inverse proportion, or neither.

1. x 7 9 15

y 3.5 4.5 7.5

2.

1

0 1

2

2

3

3

4

4

y

x

3.

3

0

6

1

9

12

2

y

x

4. y � 4x � 3 5. 2y � 15

x

Find the constant of proportionality. Then write an equation relating x and y.

6. y is directly proportional to x, and y � 35 when x � 7.

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Assessments Course 2 49

Solve using proportional reasoning.

7. y is directly proportional to x, and y � 216 when x � 2.

a) Find y when x � 7.

b) Find x when y � 540.

8. r is inversely proportional to s, and s � 30 when r � 10.

a) Write an equation relating r and s.

b) Find s when r � 150.

Problem Solving (Question 9: 2 points, Questions 10 to 12: 3 � 3 points � 9 points, Question 13: 4 points)

Use a proportion to solve each question. Show your work.

9. The circumference, C, of a circle is directly proportional to the diameter, d, of a circle. They are related by the formula C � d.

a) Find the constant of proportionality in the formula.

b) What is the diameter of a circle with circumference 105 centimeters? Round your answer to the nearest tenth. Use 3.14 as an approximation for .

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10. The volume of paint used, V liters, is directly proportional to the area, A square feet, that the paint can cover. 5 liters of paint can cover a wall with an area of 75 square feet.

a) Find the constant of proportionality.

b) Write an equation relating V and A.

c) How much paint would be needed to cover an area of 180 square feet?

11. Jane paints clay figurines to sell at a crafts fair. The graph shows that the number of figurines she paints, y, is directly proportional to the number of days she paints, x.

Painting Clay Figurines

Number of Days

Num

ber

of

Cla

y Fi

gur

ines

0x

y

5

1

10

2

15

3

20

4

25

5

30

6

a) Find the constant of proportionality.

b) What does the constant of proportionality represent in this situation?

c) How long will it take Jane to paint 30 figurines?

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12. The table shows the daily houseboat rental rate, in P dollars, for x number of people.

Number of People (x) 1 2 3

Rental Rate (P dollars per person) 240 120 80

a) Describe the relationship between the number of people and the daily houseboat rental rate.

b) Write an equation relating x and P.

c) What is the rental rate, in dollars per person, if 6 people plan to rent the houseboat?

13. The time taken to cycle a particular distance varies inversely with the speed of the bicycle. Tim takes 3 hours to reach his destination traveling at a constant speed of 12 miles per hour.

a) Find the constant of proportionality.

b) What does the constant of proportionality represent in the context of the problem?

c) Write an equation relating speed and time.

d) How long would it take Tim to reach his destination if he travels at a constant speed of 15 miles per hour?

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CHAPTER TEST B

Direct and Inverse Proportion5

Concepts and Skills (Questions 1 to 6: 6 � 1 point � 6 points, Questions 7 and 8: 2 � 2 points � 4 points)

Tell whether each table, graph, or equation represents a direct proportion, an inverse proportion, or neither.

1. x 2 4 8

y 15 712

334

2.

1

0 1

2

2

3

3

4

4

y

x

3. xy � 18 4. y � 2.25x

Find the constant of proportionality for each situation. Then write an equation relating x and y.

5. x is inversely proportional to y, and x � 9 when y � 4.

6. y is directly proportional to x in the table shown below.

x 2 3 5

y 5 712

1212

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Assessments Course 2 53

Solve using proportional reasoning.

7. p is directly proportional to m, and p � 128 when m � 8.

a) Find p when m � 10.

b) Find m when p � 80.

8. x is inversely proportional to y, and x � 18 when y � 4.

a) Write an equation relating x and y.

b) Find x when y � 30.

Problem Solving (5 � 3 points � 15 points)

Use a proportion to solve each question. Show your work.

9. The cost of a piece of ribbon, c, is directly proportional to the length of the ribbon, r. The cost of 8 meters of ribbon is $5.60.

a) Find the cost per meter of the ribbon.

b) Write an equation relating c and r.

c) Find the value of c when r is 9.

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10. The table below shows the relationship between mass in grams and mass in ounces. The mass in grams is directly proportional to the mass in ounces.

Mass (x ounces) 2 4 6

Mass (y grams) 56.7 113.4 170.1

a) Find the constant of proportionality.

b) Write a direct proportion equation.

c) How many grams are in 7 ounces?

11. M varies inversely as N, and M � 60 when N � 2.

a) Find the constant of proportionality.

b) Write an equation relating N and M.

c) Find the value of M when N � 5.

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Assessments Course 2 55

12. The graph below shows the exchange rate between U.S. dollars (USD) and Thailand baht (THB).

Currency Exchange Rates

U.S. Dollars

Thai

land

Bah

t

x

y

70 62 4 531

30

150

180

210

90

60

120

a) What is the exchange rate when you convert U.S. dollars to Thailand baht?

b) Sam wants to exchange 120 Thailand baht for U.S. dollars. Find the amount of U.S. dollars he will receive.

c) Dave wishes to exchange 7 U.S. dollars for Thailand baht. Find the amount of Thailand baht he will receive.

13. The number of students, n, is inversely proportional to the time, t days, required to complete a project. It takes 12 students 20 days to complete a project.

a) Find the constant of proportionality.

b) Write an inverse proportion equation.

c) Find the number of days it would take for 15 students to complete the same project.

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Assessments Course 2 179

5. q � �113

10�11��2

13

6. x �2

�4 �3 �2 �1�5

7. y � 312

6543312

8. p �5

�8 �7 �6 �5 �4

9. 39 in. 10. $611. b � 4112. 51 bags of popcorn13. At least 22 points14. At least 4 computers

Chapter 5 Pre-Test

1. 4 : 5 2. 5 : 8 3. Yes 4. Yes 5. No 6. No 7. Yes; Sample: 14 : 30; 21 : 45 8. No; Sample: 3 : 9; 1 : 3

9. Yes; Sample: 2224

; 3336

10. Yes; Sample: 1018

; 1527

11. 5.7 m/s

12. A: $0.26/fl oz; B: $0.23/fl oz; B is the better buy.

13. A: $1.07 per oz; B: $1.06 per oz; B is the better buy.

14. A(4, 3); B(3, 4); C(1, 2); D(5, 1)

15. 780 girls

16. $21.25

Chapter 5 Test A

1. Direct proportion 2. Neither 3. Inverse proportion

4. Neither

10.

0 1 2 3 414

11.

�7 �6 �5 �4 �3

12.

14 15 16 17 18

13. � 14. �

15. � 16. �

17. x ≤ 50,000 18. x ≥ 45

19. x ≤ 300 20. x � 10

21. x ≥ 18 22. x � 95

23. x � 150 24. x � 500

25. x ≤ 2,000

Chapter 4 Test A

1. x � 4 2. m � 20

3. r � 5 4. a � 2

5. y �12

�4 �3 �2 �1 0�12

6. x � 34

�3 �2 �1 0 1

34

7. y 12

43210 1

2

8. x � 1

43210

9. $0.55 10. 45 people

11. x � 32 12. At least 97

13. At most 33 students

14. x � 30

Chapter 4 Test B

1. m � 3 2. x � 2

3. y � �40 4. p � 6

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180 Answers

5. Direct proportion

6. 5; y � 5x 7. a) y � 756

b) x � 5

8. a) sr � 300 b) s � 2

9. a) , 227

or 3.14

b) 33.4 cm

10. a) 1

15

b) V � 1

15 A

c) 12 L

11. a) 5 b) It represents the number of clay figurines

she paints per day. c) 6 days

12. a) The value of x increases as the value of P decreases, and the product of x and P is a constant value. Hence, the rental rate is inversely proportional to the number of people renting the houseboat.

b) xP � 240 c) $40

13. a) 36 b) It represents the distance traveled. c) st � 36 d) 2.4 h

Chapter 5 Test B

1. Inverse proportion

2. Neither

3. Inverse proportion

4. Direct proportion

5. 36; xy � 36

6. 2.5; y � 2.5x 7. a) p � 160 b) m � 5

8. a) xy � 72 b) x � 2.4

9. a) $0.70 b) c � 0.7r c) c � 6.3

10. a) 28.35 b) y � 28.35x c) 198.45 g

11. a) 120 b) NM � 120 c) M � 24

12. a) 30 Thailand baht per U.S. dollar b) 4 USD c) 210 THB

13. a) 240 b) nt � 240 c) 16 days

Mid-Course Test A

1. B 2. C

3. D 4. B

5. C 6. B

7. B 8. A

9. D 10. A

11. 2,100 mi

12. 0.55p � 12q13. y 6

14. x � 1

15. 11x

16. 3 45

� p

17. 4 � 4 871, � 32.4 � �2325

� �638

18. 12°F

19. a) 3,240 ft b) 194,400 ft

20. $(2.4x � 0.45y � 2.2)

21. 190

22. x � 6

23. a) One floor above ground level b) $270

24. a) 18

34

168 76x x� ( )− �

b) 80 g c) 8 g

25. a) Direct proportion b) 3; The cost of 1 pen is $3.

c) y � 3x d) It means the cost of 4 pens is $12. e) 8 pens

26. a) i) Mount Whitney, California ii) Death Valley, California b) 6,317 ft c) Death Valley, California d) Houston, Texas

27. 13 nickel coins

28. a) (258 � 2.1v) mi b) 132 mi

29. 7

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