Chapter 7 11 25 40 25 11. 40 = ... 23. 18 422 8% 8 100 100 4 25 25 ... Chapter 7: Percent ISM:...

340

Chapter 7

Section 7.1

Practice Problems

1. Since 27 students out of 100 students in a club

are freshman, the fraction is 27 .

100 Then

27 27%.100

=

2. 31 31%

100=

3. 49% = 49(0.01) = 0.49

4. 3.1% = 3.1(0.01) = 0.031

5. 175% 175(0.01) = 1.75

6. 0.46% = 0.46(0.01) = 0.0046

7. 600% = 600(0.01) = 6.00 or 6

8. 1 50 1 50 150% 50

100 100 2 50 2⋅

= ⋅ = = =⋅

9. 1 2.3 2.3 10 232.3% 2.3

100 100 100 10 1000⋅

= ⋅ = = =⋅

10. 1 150 3 50 3 1150% 150 or 1

100 100 2 50 2 2⋅

= ⋅ = = =⋅

11. 2 2 166 % 663 3 100

200 13 100

2 100 13 100

23

= ⋅

= ⋅

⋅= ⋅

=

12. 1 12 3 4 312% 12

100 100 25 4 25⋅

= ⋅ = = =⋅

13. 0.14 = 0.14(100%) = 14.% or 14%

14. 1.75 = 1.75(100%) = 175.% or 175%

15. 0.057 = 0.057(100%) = 05.7% or 5.7%

16. 0.5 = 0.5(100%) = 050.% or 50%

17. 1 1 1 100 100100% % % 25%4 4 4 1 4= ⋅ = ⋅ = =

18. 9 9 100%40 40

9 100 %40 1900 %40

2022 %40122 %2

= ⋅

= ⋅

=

=

=

19. 1 1152 2

11 100%2

11 100 %2 1

1100 %2

550%

=

= ⋅

= ⋅

=

=

20. 3 3 3 100% 300100% % 17.65%

17 17 17 1 17= ⋅ = ⋅ = ≈

17.646 17.6517 300.000

17130119

11 010 2

8068120

≈

−

−

−

−

Thus, 3

17 is approximately 17.65%.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall

ISM: Prealgebra Chapter 7: Percent

341

21. As a decimal 27.5% = 27.5(0.01) = 0.275.

As a fraction 127.5% 27.5

10027.510027.5 10100 10275

100011 2540 2511 .40

= ⋅

=

= ⋅

=

⋅=

⋅

= Thus, 27.5% written as a decimal is 0.275, and

written as a fraction is 11 .40

22. 3 7 7 7 100% 7001 100% % 175%4 4 4 4 1 4= = ⋅ = ⋅ = =

Thus, a “134

times” increase is the same as a

“175% increase.”

Vocabulary and Readiness Check

1. Percent means “per hundred.”

2. 100% = 1.

3. The % symbol is read as percent.

4. To write a decimal or a fraction as a percent, multiply by 1 in the form of 100%.

5. To write a percent as a decimal, drop the % symbol and multiply by 0.01.

6. To write a percent as a fraction, drop the %

symbol and multiply by 1 .

100

Exercise Set 7.1

1. 96 96%

100=

2. 81 81%

100=

3. 37 out of 100 adults preferred football. 37 37%

100=

4. Only 3 out of 100 adults preferred volleyball. 3 3%

100=

5. 37 of the adults preferred football, while 13 preferred soccer. Thus, 37 + 13 = 50 preferred football or soccer. 50 50%

100=

6. 20 of the adults preferred basketball, while 15 preferred baseball. Thus, 20 + 15 = 35 preferred basketball or baseball. 35 35%

100=

7. 41% = 41(0.01) = 0.41

8. 62% = 62(0.01) = 0.62

9. 6% = 6(0.01) = 0.06

10. 3% = 3(0.01) = 0.03

11. 100% = 100(0.01) = 1.00 or 1

12. 136% = 136(0.01) = 1.36

13. 73.6% = 73.6(0.01) = 0.736

14. 45.7% = 45.7(0.01) = 0.457

15. 2.8% = 2.8(0.01) = 0.028

16. 1.4% = 1.4(0.01) = 0.014

17. 0.6% = 0.6(0.01) = 0.006

18. 0.9% = 0.9(0.01) = 0.009

19. 300% = 300(0.01) = 3.00 or 3

20. 500% = 500(0.01) = 5.00 or 5

21. 32.58% = 32.58(0.01) = 0.3258

22. 72.18% = 72.18(0.01) = 0.7218

23. 1 8 4 2 28% 8

100 100 4 25 25⋅

= ⋅ = = =⋅

24. 1 22 2 11 1122% 22

100 100 2 50 50⋅

= ⋅ = = =⋅


Chapter 7: Percent ISM: Prealgebra

342

25. 1 4 1 4 14 4

100 100 4 25 25⋅

= ⋅ = = =⋅

%

26. 1 2 2 1 12% 2

100 100 2 50 50⋅

= ⋅ = = =⋅

27.

14.5% 4.5100

4.51004.5 10100 10

451000

5 95 200

9200

= ⋅

=

⋅=

⋅

=

⋅=

⋅

=

28.

17.5% 7.5100

7.51007.5 10100 10

7510003 25

40 253

40

= ⋅

=

⋅=

⋅

=

⋅=

⋅

=

29. 1 175 7 25 7 3175 175 or 1

100 100 4 25 4 4⋅

= ⋅ = = =⋅

%

30. 1 275 11 25 11 3275% 275 or 2

100 100 4 25 4 4⋅

= ⋅ = = =⋅

31.

16.25% 6.25100

6.251006.25 100100 100

62510,0001 625

16 6251

16

= ⋅

=

⋅=

⋅

=

⋅=

⋅

=

32.

18.75% 8.75100

8.751008.75 100100 100

87510,0007 125

80 1257

80

= ⋅

=

⋅=

⋅

=

⋅=

⋅

=

33. 1 1 1 31 1 3110 103 3 100 3 100 300

= ⋅ = ⋅ =%

34. 3 3 1 31 1 317 % 74 4 100 4 100 400

= ⋅ = ⋅ =

35. 3 3 1 179 1 17922 % 228 8 100 8 100 800

= ⋅ = ⋅ =

36. 7 7 121 % 218 8 100

175 18 100

1758007 25

32 257

32

= ⋅

= ⋅

=

⋅=

⋅

=

37. 0.006 = 0.006(100%) = 0.6%

38. 0.008 = 0.008(100%) = 0.8%

39. 0.22 = 0.22(100%) = 22%

40. 0.44 = 0.44(100%) = 44%

41. 5.3 = 5.3(100%) = 530%

42. 2.7 = 2.7(100%) = 270%

43. 0.056 = 0.056(100%) = 5.6%

44. 0.019 = 0.019(100%) = 1.9%

45. 0.2228 = 0.2228(100%) = 22.28%

46. 0.1115 = 0.115(100%) = 11.15%



343

47. 3.00 = 3.00(100%) = 300%

48. 9.00 = 9.00(100%) = 900%

49. 0.7 = 0.7(100%) = 70%

50. 0.8 = 0.8(100%) = 80%

51. 7 7 700100% % 70%

10 10 10= ⋅ = =

52. 9 9 900100% % 90%

10 10 10= ⋅ = =

53. 4 4 400100 805 5 5= ⋅ = =% % %

54. 2 2 200100% % 40%5 5 5= ⋅ = =

55. 34 34 3400100% % 68%50 50 50

= ⋅ = =

56. 41 41 4100100% % 82%50 50 50

= ⋅ = =

57. 3 3 300 75 1100 378 8 8 2 2= ⋅ = = =% % % %

58. 5 5 500 125 1100% % % 31 %

16 16 16 4 4= ⋅ = = =

59. 1 1 100 1100% % 33 %3 3 3 3= ⋅ = =

60. 2 2 200 2100% % 66 %3 3 3 3= ⋅ = =

61. 1 1 9004 4 100 100%2 2 2= ⋅ ⋅ =

9% = % = 450%

2

62. 1 1 31 31006 6 100% 100% % 620%5 5 5 5= ⋅ = ⋅ = =

63. 9 9 19 19001 1 100% 100% % 190%

10 10 10 10= ⋅ = ⋅ = =

64. 7 7 27 27002 2 100% 100% 270%

10 10 10 10= ⋅ = ⋅ = =

65. 9 9 10011 11

= ⋅900

% = %11

81.818 81.8211 900.000

8820119 08 8

201190882

≈

−

−

−

−

−

911

is approximately 81.82%.

66. 11 11 1100100% %12 12 12

= ⋅ =

91.666 91.6712 1100.000

10820128 07 2

8072

80

≈

−

−

−

−

1112


67. 4 4 400100% %

15 15 15= ⋅ =

26.666 26.6715 400.000

30100

9010 09 01 00

9010

≈

−

−

−

−

415




344

68. 10 10 1000100% %11 11 11

= ⋅ =

90.909 90.9111 1000.000

9910 0

9 9100

991

≈

−

−

−

1011


69. Percent Decimal Fraction

60% 0.6 35

1223 % 0.235

47200

80% 0.8 45

1333 % 0.3333 1

3

87.5% 0.875 78

7.5% 0.075 3

40


52.5% 0.525 2140

75% 0.75 34

1266 % 0.665

133200

1383 % 0.8333

56

100% 1 1

14% 0.14 7

50


200% 2 2

280% 2.8 452

705% 7.05 1207

454% 4.54 27504


800% 8 8

320% 3.2 153

608% 6.08 2256

926% 9.26 13509

73. 38% = 38(0.01) = 0.38

1 38 1938 38100 100 50

= ⋅ = =%

74. 56% = 56(0.01) = 0.56 1 56 1456% 56

100 100 25= ⋅ = =

75. 25.2% = 25.2(0.01) = 0.252 125.2% 25.2

10025.210025.2 10100 10252

100063

250

= ⋅

=

⋅=

⋅

=

=



345

76. 28.5% = 28.5(0.01) = 0.285 128.5% 28.5

10028.510028.5 10100 10285

100057200

= ⋅

=

= ⋅

=

=

77. 32.2% = 32.2(0.01) = 0.322 132.2 32.2

10032.210032.2 10100 10322

1000161500

= ⋅

=

= ⋅

=

=

%

78. 14.8% = 14.8(0.01) = 0.148 114.8% 14.8

10014.810014.8 10100 10148

100037250

= ⋅

=

⋅=

⋅

=

=

79. 0.4% = 0.4(0.01) = 0.004 10.4% 0.4

1000.41000.4 10100 10

41000

1250

= ⋅

=

= ⋅

=

=

80. 58.3% = 58.3(0.01) = 0.583 1 58.3 58.3 10 58358.3% 58.3

100 100 100 10 1000= ⋅ = = ⋅ =

81. 12% = 12(0.01) = 0.12 1 12 312 12

100 100 25= ⋅ = =%

82. 7.1% = 7.1(0.01) = 0.071 1 7.1 7.1 10 717.1% 7.1

100 100 100 10 1000= ⋅ = = ⋅ =

83. 0.442 = 0.442(100%) = 44.2%

84. 0.347 = 0.347(100%) = 34.7%

85. 7 7 700(100 ) % 0.7%

1000 1000 1000= = =

7% % =

10

86. 3 3 300 6100% % % 1.2%

250 250 250 5= ⋅ = = =

87. 1 3.9 3.9 10 393.9% 3.9

100 100 100 10 1000= ⋅ = = ⋅ =

88. 1 12.9 12.9 10 12912.9% 12.9

100 100 100 10 1000= ⋅ = = ⋅ =

89.

3 1 8 3 1 84 2 9 4 2 9

3 1 2 44 2 93 44 93 9 4 44 9 9 427 1636 3627 16

361136

⋅− ⋅ = −

⋅⋅ ⋅

= −⋅

= −

= ⋅ − ⋅

= −

−=

=

90. 2 5 2 5 7 3

11 11 11 11 11 117 3

11 1121

121

⎛ ⎞⎛ ⎞ ⎛ ⎞⎛ ⎞+ − = −⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠ ⎝ ⎠⎝ ⎠

⋅= −

⋅

= −



346

91. 2 5 20 296 43 6 3 6

20 2 293 2 6

40 296 6

116516

− = −

= ⋅ −

= −

=

=

92. 2 5 20 296 43 6 3 6

20 63 2920 2 33 29

402911129

÷ = ÷

= ⋅

⋅ ⋅=

⋅

=

=

93. a. 52.8647% rounded to the nearest tenth of a percent is 52.9%.

b. 52.8647% rounded to the nearest hundredth of a percent is 52.86%.

94. a. 0.5269% rounded to the nearest tenth of a percent is 0.5%.

b. 0.5269% rounded to the nearest hundredth of a percent is 0.53%.

95. a. 6.5% = 6.5(0.01) = 0.065 INCORRECT

b. 7.8% = 7.8(0.01) = 0.078 CORRECT

c. 120% = 120(0.01) = 1.20 INCORRECT

d. 0.35% = 0.35(0.01) = 0.0035 CORRECT

b and d are correct.

96. a. 0.231 = 0.231(100%) = 23.1% CORRECT

b. 5.12 = 5.12(100%) = 512% INCORRECT

c. 3.2 = 3.2(100%) = 320% CORRECT

d. 0.0175 = 0.0175(100%) = 1.75% INCORRECT

a and c are correct.

97. 45% + 40% + 11% = 96% 100% − 96% = 4% 4% of the U.S. population have AB blood type.

98. 45% + 30% + 20% = 95% 100% − 95% = 5% Other is 5% of the top four components of bone.

99. 3 of 4 equal parts are shaded, so 3 3 300100% % 75%4 4 4= ⋅ = =

100. 5 of 8 equal parts are shaded so 5 5 500100% % 62.5%8 8 8= ⋅ = =

101. A fraction written as a percent is greater than 100% when the numerator is greater than the denominator.

102. A decimal written as a percent is less than 100% when the decimal is less than 1.

103. 21 0.2658 0.26679

≈ ≈

0.2658(100%) = 26.58% ≈ 26.6%

104. 56 0.5490 0.549

102≈ ≈

0.549(100%) = 54.9%

105. The longest bar corresponds to network systems and data communication analysts, so that is predicted to be the fastest growing occupation.

106. The second longest bar corresponds to medical assistants, so that is predicted to be the second fastest growing occupation.

107. The percent change for physicians assistants is 49%, so 49% = 49(0.01) = 0.49.

108. The percent change for medical assistants is 54%, so 54% = 54(0.01) = 0.54.

109. answers may vary




347

Section 7.2

Practice Problems

1. 8 is what percent of 48?

8 48x↓ ↓ ↓ ↓ ↓= ⋅

2. 2.6 is 40% of what number ?

2.6 40% x↓ ↓ ↓ ↓ ↓

= ⋅

3. What number is 90% of 0.045?

90% 0.045x↓ ↓ ↓ ↓ ↓

= ⋅

4. 56% of 180 is what number ?

56% 180 x↓ ↓ ↓ ↓ ↓

⋅ =

5. 12% of what number is 21?

12% 21x↓ ↓ ↓ ↓ ↓

⋅ =

6. What percent of 95 is 76?

95 76x↓ ↓ ↓ ↓ ↓

⋅ =

7. What number is 25% of 90?

25% 90x↓ ↓ ↓ ↓ ↓

= ⋅

x = 25% ⋅ 90 x = 0.25 ⋅ 90 x = 22.5 Then 22.5 is 25% of 90. Is this reasonable? To see, round 25% to 30%. Then 30% or 0.30(90) is 27. Our result is reasonable since 22.5 is close to 27.


95% 400 x↓ ↓ ↓ ↓ ↓

⋅ =

0.95 400380

xx

⋅ ==

Then 95% of 400 is 380. Is this result reasonable? To see, round 95% to 100%. Then 100% of 400 or 1.0(400) = 400, which is close to 380.

9. 15% of what number is 2.4?

15% 2.4x↓ ↓ ↓ ↓ ↓

⋅ =

0.15 2.40.15 2.40.15 0.15

16

xxxx

⋅ =

=

=

Then 15% of 16 is 2.4. Is this result reasonable? To see, round 15% to 20%. Then 20% of 16 or 0.20(16) = 3.2, which is close to 2.4.

10. 118 is 4 % of what number ?2

118 4 %2

x

↓ ↓ ↓ ↓ ↓

= ⋅

18 0.4518 0.045

0.045 0.045400

xx

x

=

=

=

Then 18 is 14 %2

of 400.


90 27x↓ ↓ ↓ ↓ ↓

⋅ =

90 2790 2790 90

310

or 0.30

xx

x

x

=

=

=

=

Since we are looking for percent, we can write 3

10 or 0.30 as a percent. x = 30%

Then 30% of 90 is 27. To check, see that 30% ⋅ 90 = 27.



348


63 45x↓ ↓ ↓ ↓ ↓= ⋅

63 4563 4545 4575

1.4140%

xx

x

xx

=

=

=

==

Then 63 is 140% of 45.


1. The word is translates to “=.”

2. The word of usually translates to “multiplication.”

3. In the statement “10% of 90 is 9,” the number 9 is called the amount, 90 is called the base, and 10 is called the percent.

4. 100% of a number = the number

5. Any “percent greater than 100%” of “a number” = “a number greater than the original number.”

6. Any “percent less than 100%” of “a number” = “a number less than the original number.”

Exercise Set 7.2


↓ ↓ ↓ ↓ ↓ 18% ⋅ 81 = x


↓ ↓ ↓ ↓ ↓ 36% ⋅ 72 = x


↓ ↓ ↓ ↓ ↓ 20% ⋅ x = 105


↓ ↓ ↓ ↓ ↓ 40% ⋅ x = 6


↓ ↓ ↓ ↓ ↓ 0.6 = 40% ⋅ x


↓ ↓ ↓ ↓ ↓ 0.7 = 20% ⋅ x

7. What percent of 80 is 3.8?

↓ ↓ ↓ ↓ ↓ x ⋅ 80 = 3.8

8. 9.2 is what percent of 92?

↓ ↓ ↓ ↓ ↓ 9.2 = x ⋅ 92


↓ ↓ ↓ ↓ ↓ x = 9% ⋅ 43


↓ ↓ ↓ ↓ ↓ x = 25% ⋅ 55


↓ ↓ ↓ ↓ ↓ x ⋅ 250 = 150


↓ ↓ ↓ ↓ ↓ x ⋅ 375 = 300

13. 10 350.10 35

3.5

xxx

⋅ =⋅ =

=

%

10% of 35 is 3.5.

14. 25 680.25 68

17

xxx

⋅ =⋅ =

=

%

25% of 68 is 17.



349

15. 14 2050.14 20528.7

xxx

= ⋅= ⋅=

%

28.7 is 14% of 205.

16. x = 18% ⋅ 425 x = 0.18 ⋅ 425 x = 76.5 76.5 is 18% of 425.

17. 1.2 121.2 0.12

1.2 0.120.12 0.12

10

xxx

x

= ⋅=

=

=

%

1.2 is 12% of 10.

18. 0.22 440.22 0.440.22 0.440.44 0.44

0.5

xxx

x

= ⋅=

=

=

%

0.22 is 44% of 0.5

19. 18 512

0.085 510.085 510.085 0.085

600

x

xx

x

⋅ =

=

=

=

%

18 %2

of 600 is 51.

20. 14 452

0.045 450.045 450.045 0.045

1000

x

xx

x

⋅ =

=

=

=

%

142

% of 1000 is 45.

21. 80 8880 88

80 801.1110

xx

xx

⋅ =⋅

=

== %

88 is 110% of 80.

22. ⋅ =⋅

=

==

40 6040 60

40 401.5150%

xx

xx

60 is 150% of 40.

23. = ⋅⋅

=

==

17 5017 50

50 500.3434%

xx

xx

17 is 34% of 50.

24. = ⋅⋅

=

==

48 5048 50

50 500.9696%

xx

xx

48 is 96% of 50.

25. = ⋅=

=

=

0.1 10%0.1 0.100.1 0.1

0.1 0.11

xx

x

x

0.1 is 10% of 1.

26. = ⋅=

=

=

0.5 5%0.5 0.05

0.5 0.05

0.05 0.0510

xxx

x

0.5 is 5% of 10.

27. ⋅ =⋅ =

=

150% 4301.5 430

645

xxx

150% of 430 is 645.

28. ⋅ =⋅ =

=

300% 563.00 56

168

xxx

300% of 56 is 168.



350

29. = ⋅

=

=

=

182.5 16 %

282.5 0.165

82.5 0.165

0.165 0.165500

x

xx

x

82.5 is 1

16 %2

of 500.

30. = ⋅

=

=

=

17.2 6 %

47.2 0.0625

7.2 0.0625

0.0625 0.0625115.2

x

xx

x

7.2 is 1

6 %4

of 115.2.

31. = ⋅⋅

=

==

2.58 502.58 50

50 500.05165.16%

xx

xx

2.58 is 5.16% of 50.

32. = ⋅⋅

=

==

2.64 252.64 25

25 250.1056

10.56%

xx

xx

2.64 is 10.56% of 25.

33. x = 42% ⋅ 60 x = 0.42 ⋅ 60 x = 25.2 25.2 is 42% of 60.

34. x = 36% ⋅ 80 x = 0.36 ⋅ 80 x = 28.8 28.8 is 36% of 80.

35. ⋅ =⋅

=

==

184 64.4184 64.4

184 1840.3535%

xx

xx

35% of 184 is 64.4.

36. ⋅ =⋅

=

==

120 76.8120 76.8

120 1200.6464%

xx

xx

64% of 120 is 76.8.

37. ⋅ =⋅ =

=

=

120% 421.20 42

1.2 42

1.2 1.235

xxx

x

120% of 35 is 42.

38. ⋅ ==

⋅=

=

160% 401.6 40

1.6 40

1.6 1.625

xxx

x

160% of 25 is 40.

39. ⋅ =⋅ =

=

2.4% 260.024 26

0.624

xxx

2.4% of 26 is 0.624.

40. ⋅ =⋅ =

=

4.8% 320.048 32

1.536

xxx

4.8% of 32 is 1.536.

41. ⋅ =⋅

=

==

600 3600 3

600 6000.0050.5%

xx

xx

0.5% of 600 is 3.

42. ⋅ =⋅

=

==

500 2500 2

500 5000.0040.4%

xx

xx

0.4% of 500 is 2.

43. = ⋅=

=

=

6.67 4.6%6.67 0.046

6.67 0.046

0.046 0.046145

xxx

x

6.67 is 4.6% of 145.



351

44. = ⋅=

=

=

9.75 7.5%9.75 0.075

9.75 0.075

0.075 0.075130

xxx

x

9.75 is 7.5% of 130.

45. = ⋅⋅

=

==

1575 25001575 2500

2500 25000.6363%

xx

xx

1575 is 63% of 2500.

46. = ⋅⋅

=

==

2520 35002520 3500

3500 35000.7272%

xx

xx

2520 is 72% of 3500.

47. = ⋅⋅

=

==

2 502 50

50 500.044%

xx

xx

2 is 4% of 50.

48. = ⋅⋅

=

==

2 402 40

40 400.055%

xx

xx

2 is 5% of 40.

49. =

⋅ = ⋅=

=

=

27 9

1027 10 9

270 9270 9

9 930

xxxx

x

50. =

⋅ ==

=

=

35 7

535 5 7175 7175 7

7 725

xxxx

x

51. =

⋅ = ⋅=

=

=

8

5 1111 8 511 4011 40

11 117

311

x

xxx

x

52. =

⋅ = ⋅=

=

=

6

3 1313 6 313 1813 18

13 135

113

x

xxx

x

53. =17

12 20

x

54. =20

25 10

x

55. =8 14

9 x

56. =5 15

6 x

57. ⋅ =⋅

=

=

5 325 32

5 532

5

nn

n

Choice c is correct.

58. n = 0.7 ⋅ 12 n = 0.84 Choice a is correct.

59. = ⋅⋅

=

=

0.06 70.06 7

7 70.06

7

nn

n

Choice b is correct.

60. Twenty percent of what number is eighteen and six-tenths?



352

61. What number is thirty-three and one-third percent of twenty-four?

62. Since 100% of 20 is 20, and 30 is greater than 20, x must be greater than 100%; b.

63. Since 100% of 98 is 98, the percent is 100%; a.

64. Since 85 is less than 120, the percent is less than 100%; c.

65. Since 55% is less than 100%, which is 1, 55% of 45 is less than 45; c.

66. Since 230% is greater than 100%, which is 1, 230% of 45 is greater than 45; b.

67. Since 100% is 1, 100% of 45 is equal to 45; a.

68. Since 30% is less than 100%, which is 1, 30% of y is less than y, so y is greater than 45; b.

69. Since 100% is 1, 100% of 45 is equal to 45; a.

70. Since 180% is greater than 100%, which is 1, 180% of y is greater than y, so y is less than 45; c.



73. ⋅ =⋅ =

=

1.5% 45, 7750.015 45, 775

686.625

xxx

1.5% of 45,775 is 686.625.

74. ⋅ =⋅

=

==

75,528 27,945.3675,528 27,945.36

75,528 75,5280.3737%

xx

xx

37% of 75,528 is 27,945.36.

75. = ⋅= ⋅

⋅=

=

22,113 180%22,113 1.8022,113 1.8

1.8 1.812,285

xx

x

x

22,113 is 180% of 12,285.

The Bigger Picture

1. ⋅ ⋅

+ = + = + =⋅ ⋅

2 1 2 5 1 9 10 9 19

9 5 9 5 5 9 45 45 45

2. 42 ÷ 2 ⋅ 3 = 21 ⋅ 3 = 63

3. −0.03(0.7) = −0.021

4. + = + =49 1 7 1 8

5. =

⋅ = ⋅=

=

=

3

8 1283 128 8

384 8384 8

8 848

n

nnn

n

6. =

⋅ = ⋅=

=

=

7.2 36

87.2 8 3657.6 3657.6 36

36 361.6

nn

nn

n

7. = ⋅⋅

=

==

215 86215 86

86 862.5

250%

xx

xx

215 is 250% of 86.

8. ⋅ ===

95% 480.95(48)

45.6

xxx

95% of 48 is 45.6 or 3

45 .5

9. = ⋅⋅

=

==

4.2 154.2 15

15 150.2828%

xx

xx

4.2 is 28% of 15.

10. = ⋅= ⋅

=

=

93.6 52%93.6 0.5293.6 0.52

0.52 0.52180

xx

x

x

93.6 is 52% of 180.



353

Section 7.3

Practice Problems


↓ ↓ ↓

percent baseIt appears afterthe word .of

amountIt is the partcompared to

the whole

=54 27

100b


↓ ↓ ↓ amount percent base

=30

90 100

p



=25

116 100

a

4. 680 is 65% of what number ?


=680 65

100b


↓ ↓ ↓ percent base amount 7540 100

p=


↓ ↓ ↓ percent base amount

4680 100a=



8120 100100 120 8

100 960100 960100 100

9.6

a

aaa

a

=

⋅ = ⋅=

=

=

9.6 is 8% of 120.



52 65100

52 100 655200 655200 65

65 6580

bbbb

b

=

⋅ = ⋅=

=

=

Thus, 65% of 80 is 52.



= =

⋅ = ⋅=

15.4 5 15.4 1 or

100 2015.4 20 1

308

b bb

b

So, 154 is 5% of 308.



8 1 or 40 100 5 100

1 100 5100 5100 5

5 520

p p

ppp

p

= =

⋅ = ⋅=

=

=

So, 20% of 40 is 8.



354



=

⋅ = ⋅=

=

=

414

180 100414 100 180

41,400 18041,400 180

180 180230

p

ppp

p

Then 414 is 230% of 180.


1. When translating the statement “20% of 15 is 3” to a proportion, the number 3 is called the amount, 15 is the base, and 20 is the percent.

2. In the question “50% of what number is 28?”, which part of the percent proportion is unknown? base

3. In the question “What number is 25% of 200?”, which part of the percent proportion is unknown? amount

4. In the question “38 is what percent of 380?”, which part of the percent proportion is unknown? percent

Exercise Set 7.3


↓ ↓ ↓ percent base amount = a

=98

45 100

a


↓ ↓ ↓ percent base amount = a

=92

30 100

a


↓ ↓ ↓ amount = a percent base

=4

150 100

a


↓ ↓ ↓ amount = a percent base

=7

175 100

a


↓ ↓ ↓ amount percent base = b

=14.3 26

100b


↓ ↓ ↓ amount percent base = b

=1.2 47

100b


↓ ↓ ↓ percent base = b amount

=84 35

100b


↓ ↓ ↓ percent base = b amount

=520 84

b b


↓ ↓ ↓ percent = p base amount

=70

400 100

p



355


↓ ↓ ↓ percent = p base amount

=216

900 100

p


↓ ↓ ↓ amount percent = p base 8.282 100

p=


↓ ↓ ↓ amount percent = p base 9.696 100

p=

13. =

⋅ = ⋅=

=

=

40

65 100100 65 40

100 2600100 2600

100 10026

a

aaa

a

40% of 65 is 26.

14. 25

84 1001

84 44 1 84

4 844 844 4

21

a

a

aaa

a

=

=

⋅ = ⋅=

=

=

25% of 84 is 21.

15. =

⋅ = ⋅⋅ =⋅

=

=

18

105 100100 18 105100 1890100 1890

100 10018.9

a

aaa

a

18.9 is 18% of 105.

16. =

⋅ = ⋅⋅ =⋅

=

=

60

29 100100 29 60100 1740100 1740

100 10017.4

a

aaa

a

17.4 is 60% of 29.

17. =

⋅ = ⋅=

=

=

90 15

10090 100 15

9000 159000 15

15 15600

bb

bb

b

15% of 600 is 90.

18. =

⋅ = ⋅=

=

=

55 55

10055 100 55

5500 555500 55

55 55100

bb

bb

b

55% of 100 is 55.

19. =

⋅ = ⋅= ⋅

⋅=

=

7.8 78

1007.8 100 78

780 78780 78

78 7810

bbbb

b

7.8 is 78% of 10.

20. =

⋅ = ⋅= ⋅

⋅=

=

1.1 44

1001.1 100 44

110 44110 44

44 442.5

bbbb

b

1.1 is 44% of 2.5.



356

21. =

⋅ = ⋅=

=

=

42

35 10042 100 35

4200 354200 35

35 35120

p

ppp

p

42 is 120% of 35.

22. =

⋅ = ⋅=

=

=

147

98 100147 100 98

14,700 9814,700 98

98 98150

p

ppp

p

147 is 150% of 98.

23. =

⋅ = ⋅=

=

=

14

50 10014 100 50

1400 501400 50

50 5028

p

ppp

p

14 is 28% of 50.

24. =

⋅ = ⋅=

=

=

24

50 10024 100 50

2400 502400 50

50 5048

p

ppp

p

24 is 48% of 50.

25. =

⋅ = ⋅=

=

=

3.7 10

1003.7 100 10

370 10370 10

10 1037

bb

bb

b

3.7 is 10% of 37.

26. =

⋅ = ⋅=

=

=

7.4 5

1007.4 100 5

740 5740 5

5 5148

bbbb

b

7.4 is 5% of 148.

27. 2.4

70 100100 70 2.4

100 168100 168100 100

1.68

a

aaa

a

=

⋅ = ⋅=

=

=

1.68 is 2.4% of 70.

28. 2.5

90 100100 90 2.5

100 225100 225100 100

2.25

a

aaa

a

=

⋅ = ⋅=

=

=

2.25 is 2.5% of 90.

29. =

⋅ = ⋅=

=

=

160 16

100160 100 16

16,000 1616,000 16

16 161000

bb

bb

b

160 is 16% of 1000.

30. =

⋅ = ⋅=

=

=

30 6

10030 100 6

3000 63000 6

6 6500

bb

bb

b

30 is 6% of 500.



357

31. =

⋅ = ⋅=

=

=

394.8

188 100394.8 100 188

39,480 18839,480 188

188 188210

p

ppp

p

394.8 is 210% of 188.

32. =

⋅ = ⋅= ⋅

⋅=

=

550.4

172 100550.4 100 172

55,040 17255,040 172

172 172320

p

ppp

p

550.4 is 320% of 172.

33. =

⋅ = ⋅=

=

=

89

62 100100 62 89

100 5518100 5518

100 10055.18

a

aaa

a

55.18 is 89% of 62.

34. =

⋅ = ⋅=

=

=

53

130 100100 130 53

100 6890100 6890

100 10068.9

a

aaa

a

68.9 is 53% of 130.

35. 2.76 100

2.7 100 6270 6270 66 645

p

ppp

p

=

⋅ = ⋅=

=

=

45% of 6 is 2.7.

36. 1.65 100

1.6 100 5160 5160 5

5 532

p

ppp

p

=

⋅ = ⋅=

=

=

32% of 5 is 1.6.

37. =

⋅ = ⋅=

=

=

105 140

100105 100 140

10,500 14010,500 140

140 14075

bb

bb

b

140% of 75 is 105.

38. =

⋅ = ⋅=

=

=

221 170

100221 100 170

22,100 17022,100 170

170 170130

bb

bb

b

170% of 130 is 221.

39. 1.8

48 100100 48 1.8

100 86.4100 86.4100 100

0.864

a

aaa

a

=

⋅ = ⋅=

=

=

1.8% of 48 is 0.864.

40. 7.8

24 100100 24 7.8

100 187.2100 187.2100 100

1.872

a

aaa

a

=

⋅ = ⋅=

=

=

7.8% of 24 is 1.872.



358

41. =

⋅ = ⋅=

=

=

4

800 1004 100 800

400 800400 800

800 8000.5

p

ppp

p

0.5% of 800 is 4.

42. 3

500 1003 100 500

300 500300 500500 5000.6

p

ppp

p

=

⋅ = ⋅=

=

=

0.6 percent of 500 is 3.

43. =

⋅ = ⋅=

=

=

3.5 2.5

1003.5 100 2.5

350 2.5350 2.5

2.5 2.5140

bb

bb

b

3.5 is 2.5% of 140.

44. =

⋅ = ⋅=

=

=

9.18 6.8

1009.18 100 6.8

918 6.8918 6.8

6.8 6.8135

bb

bb

b

9.18 is 6.8% of 135.

45. =

⋅ = ⋅=

=

=

20

48 100100 48 20

100 960100 960

100 1009.6

a

aaa

a

20% of 48 is 9.6.

46. =

⋅ = ⋅=

=

=

75

14 100100 14 75

100 1050100 1050

100 10010.50

a

aaa

a

75% of 14 is 10.5.

47. =

⋅ = ⋅=

=

=

2486

2200 1002486 100 2200

248,600 2200248,600 2200

2200 2200113

p

ppp

p

2486 is 113% of 2200.

48. =

⋅ = ⋅=

=

=

9310

3800 1009310 100 3800

931,000 3800931,000 3800

3800 3800245

p

ppp

p

9310 is 245% of 3800.

49. − − − ⋅⎛ ⎞− + − = = = − = −⎜ ⎟ ⋅⎝ ⎠

11 3 11 3 14 2 7 7

16 16 16 16 2 8 8

50. ⋅ ⋅ −

− = − = − = = −⋅ ⋅

7 5 7 2 5 3 14 15 14 15 1

12 8 12 2 8 3 24 24 24 24

51.

− = −

⋅= −

⋅

= −

−=

=

=

=

1 11 7 113

2 30 2 307 15 11

2 15 30105 11

30 30105 11

3094

304

3302

315



359

52. + = +

⋅ ⋅= +

⋅ ⋅

= +

=

=

2 1 8 92 4

3 2 3 28 2 9 3

3 2 2 316 27

6 643

61

76

53.

1

0.410.290.70

54.

+

1

10.784.300.21

15.29

55. −

2.380.19

2.19

56. −16.37

2.61

13.76



59. =

⋅ ⋅=

25

64 10017 25

64 10017 100 25 64

1700 1600 False

a

�

�

The amount is not 17.

=

⋅ = ⋅=

=

=

25

64 100100 25 64

100 1600100 1600

100 10016

a

aaa

a

25% of 64 is 16.

60. =

⋅ ⋅=

520 65

100520 65

800 100520 100 800 65

52,000 52,000 True

b

�

�

Yes the base is 80.

61. =

=

36

12 10036 50

12 1001

3 False2

p

�

The percent is not 50.

=

⋅ = ⋅=

=

=

36

12 10036 100 12

3600 123600 12

12 12300

p

ppp

p

The percent is 300 (300%).



64. =

⋅ = ⋅=

=

≈

22.3

53,862 100100 22.3 53,862

100 1,201,122.6100 1,201,122.6

100 10012,011.2

a

aaa

a

22.3% of 53,862 is 12,011.2.

65. =

⋅ = ⋅=

=

≈

88,542

110,736 10088,542 100 110, 736

8,854,200 110,7368,854,200 110, 736

110,736 110, 73679.958

p

ppp

p

80.0% of 110,736 is 88,542.



360

66. =

⋅ = ⋅=

=

≈

8652 119

1008652 100 119

865,200 119865,200 119

119 1197270.6

bb

bb

b

8652 is 119% of 7270.6.

The Bigger Picture

1. ⋅ ⋅ +

+ = + = + = =⋅ ⋅

2 1 2 5 1 9 10 9 10 9 19

9 5 9 5 5 9 45 45 45 45

2. 42 ÷ 2 ⋅ 3 = 21 ⋅ 3 = 63

3. −0.03(0.7) = −0.021

4. 7.9 + 0.1 = 8

5. =

⋅ = ⋅=

=

=

3

8 1283 128 8

384 8384 8

8 848

n

nnn

n

6. =

⋅ = ⋅=

=

=

7.2 36

87.2 8 3657.6 3657.6 36

36 361.6

nn

nn

n

7. =

⋅ = ⋅=

=

=

215

86 100215 100 86

21,500 8621,500 86

86 86250

p

ppp

p

215 is 250% of 86.

8. =

⋅ = ⋅=

=

= =

95

48 100100 95 48

100 4560100 4560

100 1006 3

45.6 or 45 4510 5

a

aaa

a

95% of 48 is 45.6 or 345 .5

9. =

⋅ = ⋅= ⋅

=

=

4.2

15 1004.2 100 15

420 15420 15

15 1528

p

pp

p

p

4.2 is 28% of 15.

10. =

⋅ = ⋅=

=

=

93.6 52

10093.6 100 52

9360 529360 52

52 52180

bb

bb

b

93.6 of 180 is 52%.

Integrated Review

1. 0.94 = 0.94(100%) = 94%

2. 0.17 = 0.17(100%) = 17%

3. = ⋅ = =3 3 300

100% % 37.5%8 8 8

4. = ⋅ = =7 7 700%

100% 350%2 2 2

5. 4.7 = 4.7(100%) = 470%

6. 8 = 8(100%) = 800%

7. = ⋅ = =9 9 900

100% % 45%20 20 20

8. = ⋅ = =53 53 5300

100% % 106%50 50 50



361

9. = = ⋅ = =3 27 27 2700

6 100% % 675%4 4 4 4

10. = = ⋅ = =1 13 13 1300

3 100% % 325%4 4 4 4

11. 0.02 = 0.02(100%) = 2%

12. 0.06 = 0.06(100%) = 6%

13. 71% = 71(0.01) = 0.71

14. 31% = 31(0.01) = 0.31

15. 3% = 3(0.01) = 0.03

16. 4% = 4(0.01) = 0.04

17. 224% = 224(0.01) = 2.24

18. 700% = 700(0.01) = 7.0

19. 2.9% = 2.9(0.01) = 0.029

20. 6.6% = 6.6(0.01) = 0.066

21. 7% = 7(0.01) = 0.07

= ⋅ =1 7

7% 7100 100

22. 5% = 5(0.01) = 0.05

= ⋅ = =1 5 1

5% 5100 100 20

23. 6.8% = 6.8(0.01) = 0.068 ⋅

= ⋅ = = = =⋅

1 6.8 6.8 10 68 176.8% 6.8

100 100 100 10 1000 250

24. 11.25% = 11.25(0.01) = 0.1125

= ⋅

=

⋅=

⋅

=

=

111.25% 11.25

10011.25

10011.25 100

100 1001125

10,0009

80

25. 74% = 74(0.01) = 0.74

= ⋅ = =1 74 37

74% 74100 100 50

26. 45% = 45(0.01) = 0.45

= ⋅ = =1 45 9

45% 45100 100 20

27. = ≈1

16 % 16.33(0.01) 0.1633

= = ⋅ =1 49 49 1 49

16 % %3 3 3 100 300

28. = ≈2

12 % 12.66(0.01) 0.1273

= = ⋅ = =2 38 38 1 38 19

12 % %3 3 3 100 300 150

29. =

⋅ = ⋅=

=

=

15

90 100100 15 90

100 1350100 1350

100 10013.5

a

aaa

a

15% of 90 is 13.5.

30. =

⋅ = ⋅=

=

=

78 78

10078 100 78

7800 787800 78

78 78100

bb

bb

b

78% of 100 is 78.

31. =

⋅ = ⋅=

=

=

297.5 85

100297.5 100 85

29, 750 8529, 750 85

85 85350

bb

bb

b

297.5 is 85% of 350.

32. =

⋅ = ⋅=

=

=

78

65 10078 100 65

7800 657800 65

65 65120

p

ppp

p

78 is 120% of 65.



362

33. =

⋅ = ⋅=

=

=

23.8

85 10023.8 100 85

2380 852380 85

85 8528

p

ppp

p

23.8 is 28% of 85.

34. =

⋅ = ⋅=

=

=

38

200 100100 38 200

100 7600100 7600

100 10076

a

aaa

a

38% of 200 is 76.

35. =

⋅ = ⋅=

=

=

40

85 100100 40 85

100 3400100 3400

100 10034

a

aaa

a

34 is 40% of 85.

36. =

⋅ = ⋅=

=

=

128.7

99 100128.7 100 99

12,870 9912,870 99

99 99130

p

ppp

p

130% of 99 is 128.7.

37. =

⋅ = ⋅=

=

=

115

250 100115 100 250

11,500 25011,500 250

250 25046

p

ppp

p

46% of 250 is 115.

38. =

⋅ = ⋅=

=

=

45

84 100100 45 84

100 3780100 3780

100 10037.8

a

aaa

a

37.8 is 45% of 84.

39. =

⋅ = ⋅=

=

=

63 42

10063 100 42

6300 426300 42

42 42150

bb

bb

b

42% of 150 is 63.

40. =

⋅ = ⋅=

=

=

58.9 95

10058.9 100 95

5890 955890 95

95 9562

bb

bb

b

95% of 62 is 58.9.

Section 7.4

Practice Problems

1. Method 1: What number is 4% of 837,000?

↓ ↓ ↓ ↓ ↓ x = 4% ⋅ 837,000 x = 0.04 ⋅ 837,000 x = 33,480 We predict 33,480 adults in Rhode Island to choose chocolate chip as their favorite ice cream. Method 2: What number is 4% of 837,000?


=

⋅ = ⋅=

=

=

4

837,000 100100 4 837,000

100 3,348,000100 3,348,000

100 10033, 480

a

aaa

a

We predict 33,480 adults in Rhode Island to choose Chocolate Chip as their favorite ice cream.



363

2. Method 1: 34,000 is what percent of 130,000?

↓ ↓ ↓ ↓ ↓ 34,000 = x ⋅ 130,000

=

=

≈=

34,000 130,00034,000 130,000

130,000 130,0000.2626%

xx

xx

In Florida, 34,000 or 26% more new nurses were needed in 2006. Method 2: 34,000 is what percent of 130,000?


=

⋅ = ⋅=

=

≈

34,000

130,000 10034,000 100 130,000

3,400,000 130,0003,400,000 130,000

130,000 130,00026

p

ppp

p

In Florida, 34,000 or 26% more new nurses were needed in 2006.

3. Method 1: 864 is 32% of what number ?

↓ ↓ ↓ ↓ ↓ 864 = 32% ⋅ x

= ⋅

=

=

864 0.32864 0.32

0.32 0.322700

xx

x

There are 2700 students at Euclid University. Method 2: 864 is 32% of what number ?


=

⋅ = ⋅=

=

=

864 32

100864 100 32

86, 400 3286, 400 32

32 322700

bb

bb

b

There are 2700 students at Euclid University.

4. What number is 20% of 202 million?

↓ ↓ ↓ ↓ ↓ x = 20% ⋅ 202 x = 0.20 ⋅ 202 x = 40.4 million

a. The increase in the number of vehicles on the road in 2004 is 40.4 million.

b. The total number of registered vehicles on the road in 2004 was 202 million + 40.4 million = 242.4 million Method 2: What number is 20% of 202 million?


=

⋅ = ⋅=

=

=

20

202 100100 20 202

100 4040100 4040

100 10040.4 million

a

aaa

a

a. The increase in the number of vehicles on the road in 2004 is 40.4 million.

b. The total number of registered vehicles on the road in 2004 was 202 million + 40.4 million = 242.4 million

5. Find the amount of increase by subtracting the original number of attendants from the new number of attendants. amount of increase = 333 − 285 = 48 The amount of increase is 48 attendants.

=

=

≈=

amount of increasepercent of increase

original amount48

2850.16816.8%

The number of attendants to the local play, Peter Pan, increased by about 16.8%.



364

6. Find the amount of decrease by subtracting 18,483 from 20,200. Amount of decrease = 20,200 − 18,483 = 1717 The amount of decrease is 1717.

=

=

==

amount of decreasepercent of decrease

original amount1717

20,2000.0858.5%

The population decreased by 8.5%.

Exercise Set 7.4

1. 4% of 220 is what number? Method 1:

⋅ =⋅ =

=

4% 2200.04 220

8.8

xxx

The minimum weight resistance is 8.8 pounds. Method 2:

=

⋅ = ⋅=

=

=

4

220 100100 220 4

100 880100 880

100 1008.8

a

aaa

a

The minimum weight resistance is 8.8 pounds.


⋅ =⋅ =

=

60% 2200.60 220

132

xxx

The maximum weight resistance is 132 pounds. Method 2:

=

⋅ = ⋅=

=

=

60

220 100100 60 220100 13,200100 13,200

100 100132

a

aaa

a

The maximum weight resistance is 132 pounds.

3. 24 is 1.5% of what number? Method 1:

= ⋅=

=

=

24 1.5%24 0.015

24 0.015

0.015 0.0151600

xxx

x

1600 bolts were inspected. Method 2:

=

⋅ = ⋅=

=

=

24 1.5

10024 100 1.5

2400 1.52400 1.5

1.5 1.51600

bb

bb

b

1600 bolts were inspected.

4. 28 is 35% of what number? Method 1:

= ⋅=

=

=

28 35%28 0.35

28 0.35

0.35 0.3580

xxx

x

80 children attend this day care center. Method 2:

=

⋅ = ⋅=

=

=

28 35

10028 100 35

2800 352800 35

35 3580

bb

bb

b

80 children attend this day care center.

5. 378 is what percent of 2700? Method 1:

= ⋅⋅

=

==

378 2700378 2700

2700 27000.1414%

xx

xx

The student spent 14% of last semester’s college cost on books.



365

Method 2:

=

⋅ = ⋅=

=

=

378

2700 100378 100 2700

37,800 270037,800 2700

2700 270014

p

ppp

p

The student spent 14% of last semester’s college cost on books.


= ⋅

=

==

154 3850154 3850

3850 38500.044%

xx

xx

Pierre received 4% of his total spending at the food cooperative as a dividend. Method 2:

=

⋅ = ⋅=

=

=

154

3850 100154 100 3850

15, 400 385015, 400 3850

3850 38504

p

ppp

p

Pierre received 4% of his total spending at the food cooperative as a dividend.


⋅ =⋅ =

=

58% 9400.58 940

545.2

xxx

545 films were rated R. Method 2:

=

⋅ = ⋅=

=

=

58

940 100100 58 940

100 54,520100 54,520

100 100545.2

a

aaa

a

545 films were rated R.


⋅ =⋅ =

=

11% 9400.11 940

103.4

xxx

103 films were rated PG-13. Method 2:

=

⋅ = ⋅=

=

=

11

940 100100 11 940

100 10,340100 10,340

100 100103.4

a

aaa

a

103 films were rated PG-13.


= ⋅⋅

=

≈≈

35 53535 535

535 5350.0656.5%

xx

xx

6.5% of the members of the 109th U.S. Congress attended a community college. Method 2:

=

⋅ = ⋅=

=

≈

35

535 10035 100 535

3500 5353500 535

535 5356.5

p

ppp

p

6.5% of the members of the 109th U.S. Congress attended a community college.

10. What percent of 54,300 is 23,200? Method 1: ⋅ =

=

≈≈

54,300 23,20054,300 23,200

54,300 54,3000.42742.7%

xx

xx

Of the 54,300 veterinarians in private practice in the United States, 42.7% are female. Method 2:

=

⋅ = ⋅=

=

≈

23,200

54,300 10023,200 100 54,300

2,320,000 54,3002,320,000 54,300

54,300 54,30042.7

p

ppp

p

Of the 54,300 veterinarians in private practice in the United States, 42.7% are female.



366


⋅ =⋅ =

=

8% 62000.08 6200

496

xxx

The decrease in the number of chairs produced is 496. The new number of chairs produced each month is 6200 − 496 = 5704 chairs. Method 2:

=

⋅ = ⋅=

=

=

8

6200 100100 8 6200100 49,600100 49,600

100 100496

a

aaa

a

The decrease in the number of chairs produced is 496. The new number of chairs produced each month is 6200 − 496 = 5704 chairs.


⋅ =⋅ =

=

5% 76400.05 7640

382

xxx

There are 382 fewer students this year. The current enrollment is 7640 − 382 = 7258 students. Method 2:

=

⋅ = ⋅=

=

=

5

7640 100100 5 7640

100 38,200100 38,200

100 100382

a

aaa

a

There are 382 fewer students this year. The current enrollment is 7640 − 382 = 7258 students.

13. What number is 49% of 63,000? Method 1: x = 49% ⋅ 63,000 x = 0.49 ⋅ 63,000 x = 30,870 The number of people employed as physician assistants is expected to be 63,000 + 30,870 = 93,870.

Method 2:

=

⋅ = ⋅=

=

=

49

63,000 100100 63,000 49

100 3,087,000100 3,087,000

100 10030,870

a

aaa

a

The number of people employed as physician assistants is expected to be 63,000 + 30,870 = 93,870.

14. 0.5% of 638,800 is what number? Method 1:

⋅ =⋅ =

=

0.5% 638,8000.005 638,800

3194

xxx

The population of North Dakota in 2000 was 638,800 + 3194 = 641,994 people. Method 2:

=

⋅ = ⋅=

=

=

0.5

638,800 100100 0.5 638,800100 319,400100 319,400

100 1003194

a

aaa

a

The population of North Dakota in 2000 was 638,800 + 3194 = 641,994 people.


= ⋅

=

==

20 4020 40

40 400.5

50%

xx

xx

50% of the total calories come from fat. Method 2:

=

⋅ = ⋅=

=

=

20

40 10020 100 40

2000 402000 40

40 4050

p

ppp

p

50% of the total calories come from fat.



367


5 205 2020 20

0.2525%

xx

xx

= ⋅

=

==

25% of the total calories come from fat. Method 2:

520 100

5 100 20500 20500 2020 2025

p

ppp

p

=

⋅ = ⋅=

=

=

25% of the total calories come from fat.


= ⋅⋅

=

==

10 8010 80

80 800.125

12.5%

xx

xx

12.5% of the total calories come from fat. Method 2:

=

⋅ = ⋅=

=

=

10

80 10010 100 80

1000 801000 80

80 8012.5

p

ppp

p

12.5% of the total calories come from fat.


= ⋅

=

≈≈

130 190130 190

190 1900.684

68.4%

xx

xx


Method 2:

=

⋅ = ⋅=

=

≈

130

190 100130 100 190

13,000 19013,000 190

190 19068.4

p

ppp

p



= ⋅

=

≈≈

35 12035 120

120 1200.292

29.2%

xx

xx


=

⋅ = ⋅=

=

≈

35

120 10035 100 120

3500 1203500 120

120 12029.2

p

ppp

p



= ⋅=

=

≈≈

35 13035 130

35 130

130 1300.269

26.9%

xxx

xx


=

⋅ = ⋅=

=

≈

35

130 10035 100 130

3500 1303500 130

130 13026.9

p

ppp

p




368

21. 26,250 is 15% of what number? Method 1:

= ⋅= ⋅

⋅=

=

26,250 15%26,250 0.1526,250 0.15

0.15 0.15175,000

xxx

x

The price of the home was $175,000. Method 2:

=

⋅ = ⋅=

=

=

26,250 15

10026,250 100 15

2,625,000 152,625,000 15

15 15175,000

bb

bb

b

The price of the home was $175,000.

22. 842.40 is 18% of what number? Method 1:

= ⋅=

=

=

842.40 18%842.40 0.18842.40 0.18

0.18 0.184680

xxx

x

The banker’s total pay is $4680. Method 2:

=

⋅ = ⋅=

=

=

842.40 18

100842.40 100 18

84,240 1884,240 18

18 184680

bb

bb

b

The banker’s total pay is $4680.

23. What number is 78% of 40? Method 1: x = 78% ⋅ 40 x = 0.78 ⋅ 40 x = 31.2 The owner can bill 31.2 hours each week for a repairman. Method 2:

=

⋅ = ⋅=

=

=

78

40 100100 78 40

100 3120100 3120

100 10031.2

a

aaa

a

The owner can bill 31.2 hours each week for a repairman.

24. What number is 1.04% of 28,350? Method 1: x = 1.04% ⋅ 28,350 x = 0.0104 ⋅ 28,350 x = 294.84 There are expected to be 295 defective components in the batch. Method 2:

=

⋅ = ⋅=

=

=

1.04

28,350 100100 1.04 28,350

100 29,484100 29,484

100 100294.84

a

aaa

a

There are expected to be 295 defective components in the batch.

25. What number is 4.5% of 19,286? Method 1: x = 4.5% ⋅ 19,286 x = 0.045 ⋅ 19,286 x = 867.87 The price of the car will increase by $867.87. The new price of that model will be $19,286 + $867.87 = $20,153.87. Method 2:

4.519,286 100

100 4.5 19,286100 86,787100 86,787100 100

867.87

a

aaa

a

=

⋅ = ⋅=

=

=

The price of the car will increase by $867.87. The new price of that model will be $19,286 + $867.87 = $20,153.87.

26. What number is 6.5% of 58,500? Method 1: x = 6.5% ⋅ 58,500 x = 0.065 ⋅ 58,500 x = 3802.5 The union worker can expect an increase of $3802.50 in salary. The new salary will be $58,500 + $3802.50 = $62,302.50.



369

Method 2:

=

⋅ = ⋅=

=

=

6.5

58,500 100100 6.5 58,500

100 380,250100 380,250

100 1003802.50

a

aaa

a

The union worker can expect an increase of $3802.50 in salary. The new salary will be $58,500 + $3802.50 = $62,302.50.

27. What number is 32% of 6950? Method 1: x = 32% ⋅ 6950 x = 0.32 ⋅ 6950 x = 2224 The number of adults in Buckeye predicted to prefer vanilla ice cream is 2224. Method 2:

=

⋅ = ⋅=

=

=

32

6950 100100 32 6950

100 222,400100 222,400

100 1002224

a

aaa

a

The number of adults in Buckeye predicted to prefer vanilla ice cream is 2224.

28. What number is 5% of 4380? Method 1: x = 5% ⋅ 4380 x = 0.05 ⋅ 4380 x = 219 The number of adults in Hamlet predicted to prefer strawberry ice cream is 219. Method 2:

=

⋅ = ⋅=

=

=

5

4380 100100 5 4380

100 21,900100 21,900

100 100219

a

aaa

a

The number of adults in Hamlet predicted to prefer strawberry ice cream is 219.

29. What number is 80% of 35? Method 1: x = 80% ⋅ 35 x = 0.80 ⋅ 35 x = 28 The increase is projected to be 28 million. The population is projected to be (35 + 28) million = 63 million. Method 2:

8035 100

100 80 35100 2800100 2800100 100

28

a

aaa

a

=

⋅ = ⋅=

=

=

The increase is projected to be 28 million. The population is projected to be (35 + 28) million = 63 million.

30. What number is 8.3% of 265,000? Method 1: x = 8.3% ⋅ 265,000 x = 0.083 ⋅ 265,000 x = 21,995 The increase is projected to be 21,995. The number of women awarded masters degrees is projected to be 265,000 + 21,995 = 286,995.

Method 2: =

⋅ = ⋅=

=

=

8.3

265,000 100100 8.3 265,000

100 2,199,500100 2,199,500

100 10021,995

a

aaa

a

The increase is projected to be 21,995. The number of women awarded masters degrees is projected to be 21,995 + 265,000 = 286,995.



370

Original

Amount New

Amount Amount of

Increase Percent Increase

31. 50 80 80 − 50 = 30 = =30

0.6 60%50

32. 8 12 12 − 8 = 4 = =4

0.5 50%8

33. 65 117 117 − 65 = 52 52 0.8 80%65

= =

34. 68 170 170 − 68 = 102 = =102

1.5 150%68

Original Amount

New Amount

Amount of Decrease

Percent Decrease

35. 8 6 8 − 6 = 2 = =2

0.25 25%8

36. 25 20 25 − 20 = 5 = =5

0.20 20%25

37. 160 40 160 − 40 = 120 120 0.75 75%160

= =

38. 200 162 200 − 162 = 38 = =38

0.19 19%200

39. =

−=

=

=

amount of decreasepercent decrease

original amount150 84

15066

1500.44

The decrease in calories is 44%.

40. =

−=

=

=



53053

5300.10

The decrease in the number of employees was 10%.



371

41. =

−=

=

≈


original amount10,845 10, 700

10,845145

10,8450.013

The decrease in cable TV systems was 1.3%.

42. =

−=

=

=

amount of increasepercent increase


3244

321.375

The increase in words per minute is 137.5%.

43. =

−=

=

≈



174270

1741.552

The increase in acres was 155.2%

44. =

−=

=

≈


original amount722.9 705.4

722.917.5

722.90.024

The decrease in CD’s shipped was 2.4%.

45. =

−=

=

≈


original amount464,000 455,000

455,0009000

455,0000.0198

The increase in computer programmers is expected to be 2%.

46. =

−=

=

≈



784108

7840.138

The decrease in boating accidents was 13.8%.

47. =

−=

=

≈



3570199

35700.056

The increase in elementary and secondary teachers is expected to be 5.6%.

48. =

−=

=

≈



484,00034,000

484,0000.070

The increase in correctional officers is expected to be 7%.

49. =

−=

=

≈



71511438

71510.201

The decrease in cinema sites was 20.1%

50. =

−=

=

=



16,00013,000

16,0000.8125

The increase in occupational therapy assistants and aides is expected to be 81.3%.



372

51. =

−=

=

≈


original amount19.9 13.1

13.16.8

13.10.519

The increase in soft drink size was 51.9%.

52. =

−=

=

=



75,000225,000

75,0003.0

The increase in discarded electronic waste was 300%.

53. =

−=

=

≈



110,000102,000

110,0000.927

The increase in cellular subscribers was 92.7%.

54. =

−=

=

≈


original amount127, 400 99,900

127, 40027,500

127, 4000.216

The decrease in the population of Tokyo is expected to be 21.6%.

55. ×

0.1238

96360

4.56

56. 0.7 29.4 becomes −

−

427 294

281414

0

57.

119.201.98

11.18+

58. −

78.0019.46

58.54

59. − − = − ⋅ − ⋅

= − −

= −

3 5 3 3 5 2

8 12 8 3 12 29 10

24 2419

24

60. ⋅ ⋅⎛ ⎞⎛ ⎞− − = = =⎜ ⎟⎜ ⎟ ⋅ ⋅ ⋅⎝ ⎠⎝ ⎠

3 5 3 5 3 5 5

8 12 8 12 8 3 4 32

61. ÷ = ÷

= ⋅

⋅=

⋅⋅ ⋅

=⋅

=

4 9 14 392 3

5 10 5 1014 10

5 3914 10

5 3914 2 5

5 3928

39

62. 4 9 4 92 3 2 35 10 5 10

⎛ ⎞− = + −⎜ ⎟⎝ ⎠

Subtract the absolute values. 93

10425

−

93

1082

1011

10

−

Attach the sign of the larger absolute value. 4 9 12 3 15 10 10− = −

63. The increased number is double the original number.




373

65. To find the percent increase, she should have divided by the original amount, which is 150.

= = =30

percent increase 0.2 20%150

66. To find the percent decrease, he should have divided by the original amount, which is 180.

−= = =

180 150 30 2percent decrease 16 %

180 180 3

67. False; the percents are different. percent increase from 1980 to 1990 = 20%

percent decrease from 1990 to 2000 = 2

16 %3

Section 7.5

Practice Problems

1. sales tax tax rate purchase price

8.5% $59.900.085 $59.90$5.09

= ⋅↓ ↓

= ⋅= ⋅≈

The sales tax is $5.09. Total Price purchase price sales tax

$59.90 $5.09$64.99

= +↓ ↓

= +=

The sales tax on $59.90 is $5.09, and the total price is $64.99.

2. sales tax tax rate purchase price

$1665 $18,5001665 18,500

18,500 18,5000.09

rr

r

= ⋅↓ ↓ ↓

= ⋅⋅

=

=

The sales tax rate is 9%.

3. = ⋅↓ ↓

= ⋅= ⋅≈

commission commission rate sales

6.6% $47,6320.066 $47,632$3143.712

The sales representative’s commission for the month is $3143.71.

4. = ⋅↓ ↓ ↓

= ⋅

=

==

commission commission rate sales

$645 $4300645

43000.1515%

r

r

rr

The commission rate is 15%.

5. = ⋅

↓ ↓= ⋅= ⋅=

amount of discountdiscount rate original price

35% $7000.35 $700$245

The discount is $245. = −

↓ ↓= −=

sale price original price discount

$700 $245$455

The sale price is $455.


1. sales tax = tax rate ⋅ purchase price.

2. total price = purchase price + sales tax.

3. commission = commission rate ⋅ sales.

4. amount of discount = discount rate ⋅ original price.

5. sale price = original price − amount of discount.

Exercise Set 7.5

1. sales tax = 5% ⋅ $150 = 0.05 ⋅ $150 = $7.50 The sales tax is $7.50.

2. = ⋅ = ⋅ =sales tax 6% $188 0.06 $188 $11.28 The sales tax is $11.28.

3. sales tax = 7.5% ⋅ $799 = 0.075 ⋅ $799 ≈ $59.93 total price = $799 + $59.93 = $858.93 The total price of the camcorder is $858.93.

4. sales tax = 8% ⋅ $426 = 0.08 ⋅ $426 = $34.08 Total price = $426 + $34.08 = $460.08 The total price of the stereo system is $460.08.



374

5. = ⋅

=

=

$335.30 $4790$335.30

$47900.07

r

r

r


6. = ⋅

=

=

$374 $6800$374

$68000.055

r

r

r

The sales tax rate is 5.5%.

7. a. = ⋅=

=

=

$10.20 8.5%$10.2 0.085$10.2

0.085$120

pp

p

p

The purchase price of the table saw is $120.

b. total price = $120 + $10.20 = $130.20 The total price of the table saw is $130.20.

8. a. = ⋅=

=

=

$76 9.5%$76 0.095

$76

0.095$800

pp

p

p

The purchase price of the ring is $800.

b. total price = $800 + $76 = $876 The total price of the ring is $876.

9. sales tax 6.5% $1800 0.065 $1800 $117= ⋅ = ⋅ = total price = $1800 + $117 = $1917 The total price of the bracelet is $1917.

10. sales tax = 8% ⋅ $1890 = 0.08 ⋅ $1890 = $151.20 total price = $1890 + $151.20 = $2041.20 The sales tax is $151.20 and the total price is $2041.20.

11. = ⋅=

=

=

$24.25 5%$24.25 0.05$24.25

0.05$485

pp

p

p

The purchase price of the futon is $485.

12. = ⋅=

=

=

$32.85 9%$32.85 0.09$32.85

0.09$365

pp

p

p

The purchase price of the TV-DVD combination is $365.

13. $98.70 $1645$98.70$1645

0.06

r

r

r

= ⋅

=

=


14. = ⋅

=

=

$103.50 $1150$103.50

$11500.09

r

r

r


15. Purchase price = $210 + $15 + $5 = $230 Sales tax = 7% ⋅ $230 = 0.07 ⋅ $230 = $16.10 Total price = $230 + $16.10 = $246.10 The sales tax is $16.10 and the total price of the items is $246.10.

16. Purchase price = $35 + $55 + $95 = $185 Sales tax = 6.5% ⋅ $185 = 0.065 ⋅ $185 ≈ $12.03 Total price = $185 + $12.03 = $197.03 The sales tax is $12.03 and the total price of the clothing is $197.03.

17. commission 4% $1,329,4010.04 $1,329,401$53,176.04

= ⋅= ⋅=

Her commission was $53,176.04.

18. = ⋅= ⋅≈

commission 12.8% $16380.128 $1638$209.66

Her commission was $209.66.

19. = ⋅

=

=

$1380.40 $9860$1380.40

$98600.14

r

r

r


20. = ⋅

=

=

$3575 $32,500$3575

$32,5000.11

r

r

r




375

21. commission 1.5% $325,9000.015 $325,900$4888.50

= ⋅= ⋅=

His commission will be $4888.50.

22. = ⋅= ⋅≈

commission 5.6% $96380.056 $9638$539.73

Her commission will be $539.73.

23. = ⋅= ⋅

=

=

$5565 3% sales$5565 0.03$5565

0.03$185,500

s

s

s

The selling price of the house was $185,500.

24. = ⋅= ⋅

=

=

$1750 7% sales$1750 0.07$1750

0.07$25,000

s

s

s

The selling price of the fertilizer was $25,000.

Original Price

Discount Rate

Amount of Discount

Sale Price

25. $89 10% 10% ⋅ $89 = $8.90 $89 − $8.90 = $80.10

26. $74 20% 20% ⋅ $74 = $14.80 $78 − $14.80 = $59.20

27. $196.50 50% 50% ⋅ $196.50 = $98.25 $196.50 − $98.25 = $98.25

28. $110.60 40% 40% ⋅ $110.60 = $44.24 $110.60 − $44.24 = $66.36

29. $410 35% 35% ⋅ $410 = 143.50 $410 − $143.50 = $266.50

30. $370 25% 25% ⋅ $370 = $92.50 $370 − $92.50 = $277.50

31. $21,700 15% 15% ⋅ $21,700 = $3255 $21,700 − $3255 = $18,445

32. $17,800 12% 12% ⋅ $17,800 = $2136 $17,800 − $2136 = $15,664

33. discount = 15% ⋅ $300 = 0.15 ⋅ $300 = $45

sale price = $300 − $45 = $255 The discount is $45 and the sale price is $255.

34. discount = 30% ⋅ $4295 = 0.30 ⋅ $4295 = $1288.50 sale price = $4295 − $1288.50 = $3006.50 The discount is $1288.50 and the sale price is $3006.50.



376

Purchase Price

Tax Rate

Sales Tax

Total Price

35. $305 9% 9% ⋅ $305 = $27.45 $305 + $27.45 = $332.45

36. $243 8% 8% ⋅ $243 = $19.44 $243 + $19.44 = $262.44

37. $56 5.5% 5.5% ⋅ $56 = $3.08 $56 + $3.08 = $59.08

38. $65 8.4% 8.4% ⋅ $65 = $5.46 $65 + $5.46 = $70.46

Sale Commission Rate Commission

39. $235,800 3% $235,800 ⋅ 3% = $7074

40. $195,450 5% $195,450 ⋅ 5% = $9772.50

41. $17,900 $1432 0.08 8%$17,900

= = $1432

42. $25,600 = =$2304

0.09 9%$25,600

$2304

43. ⋅ ⋅ = ⋅ =3

2000 2 600 2 120010

44. ⋅ ⋅ = ⋅ =2

500 3 40 3 12025

45. ⋅ ⋅ = ⋅ =3

400 11 12 11 132100

46. ⋅ ⋅ = ⋅ =1

1000 5 50 5 25020

47. ⋅ ⋅ = ⋅ =2 2

600 0.04 24 163 3

48. ⋅ ⋅ = ⋅ =3 3

6000 0.06 360 2704 4

49. Round $68 to $70 and 9.5% to 10%. 10% ⋅ $70 = 0.10 ⋅ $70 = $7 $70 + $7 = $77 The best estimate of the total price is $77; d.

50. 10% ⋅ $200 = 0.10 ⋅ $200 = $20 $200 + $20 = $220 The best estimate is c; $220.



377

Bill Amount 10% 15% 20%

51. $40.21 ≈ $40 $4.00 + = + =1

$4 ($4) $4 $2 $6.002

2($4) = $8.00

52. $15.89 ≈ $16 $1.60 + = + =1

$1.60 ($1.60) $1.60 $0.80 $2.402

2($1.60) = $3.20

53. $72.17 ≈ $72.00 $7.20 1$7.20 ($7.20) $7.20 $3.602

$10.80

+ = +

=

2($7.20) = $14.40

54. $9.33 ≈ $9 $0.90 + = + =1

$0.90 ($0.90) $0.90 $0.45 $1.352

2($0.90) = $1.80

55. A discount of 60% is better; answers may vary.

56. A discount of 20% plus an additional 40% is better. Answers may vary.

57. 7.5% ⋅ $24,966 = 0.075 ⋅ $24,966 = $1872.45 $24,966 + $1872.45 = $26,838.45 The total price of the necklace is $26,838.45.

58. = ⋅= ⋅=

commission 5.5% $562,5600.055 $562,560$30,940.80

= ⋅= ⋅=

agent's amount 60% $30,940.800.60 $30,940.80$18,564.48

The real estate agent will receive $18,564.48.

Section 7.6

Practice Problems

1. = ⋅ ⋅= ⋅ ⋅= ⋅ ⋅=

$875 7% 5$875 (0.07) 5$306.25

I P R TI

The simple interest is $306.25.

2. = ⋅ ⋅

= ⋅ ⋅

= ⋅ ⋅

=

9$1500 20%

129

$1500 (0.20)12

$225

I P R T

I

She paid $225 in interest.



378

3. = ⋅ ⋅

= ⋅ ⋅

= ⋅ ⋅

=

6$2100 13%

126

$2100 (0.13)12

$136.50

I P R T

The interest is $136.50. = += +=

total amount principal interest$2100 $136.50$2236.50

After 6 months, the total amount paid will be $2236.50.

4. P = $3000, r = 4% = 0.04, n = 1, t = 6 years ⋅

⋅

⎛ ⎞= +⎜ ⎟⎝ ⎠

⎛ ⎞= +⎜ ⎟⎝ ⎠

=≈

1 6

6

1

0.04$3000 1

1

$3000(1.04)$3795.96

n tr

A Pn

The total amount after 6 years is $3795.96.

5. P = $5500, = =1

6 % 0.0625,4

r n = 365, t = 5

⋅

⋅

⎛ ⎞= +⎜ ⎟⎝ ⎠

⎛ ⎞= +⎜ ⎟⎝ ⎠

≈

365 5

1

0.0625$5500 1

365$7517.41

n tr

A Pn

The total amount after 5 years is $7517.41.

Calculator Explorations

1. ⋅

⎛ ⎞= + ≈⎜ ⎟⎝ ⎠

4 50.09$600 1 $936.31

4A

2. ⋅

⎛ ⎞= + ≈⎜ ⎟⎝ ⎠

365150.04$10,000 1 $18,220.59

365A

3. ⋅

⎛ ⎞= + ≈⎜ ⎟⎝ ⎠

1 200.11$1200 1 $9674.77

1A

4. ⋅

⎛ ⎞= + ≈⎜ ⎟⎝ ⎠

2 10.07$5800 1 $6213.11

2A

5. ⋅

⎛ ⎞= + ≈⎜ ⎟⎝ ⎠

4 40.06$500 1 $634.49

4A

6. ⋅

⎛ ⎞= + ≈⎜ ⎟⎝ ⎠

365190.05$2500 1 $6463.85

365A


1. To calculate simple interest, use I = P ⋅ R ⋅ T.

2. To calculate compound interest, use ⋅

⎛ ⎞= +⎜ ⎟⎝ ⎠1 .

n tr

A Pn

3. Compound interest is computed on not only the original principal, but on interest already earned in previous compounding periods.

4. When interest is computed on the original principal only, it is called simple interest.

5. Total amount (paid or received) = principal + interest.

Exercise Set 7.6

1. = ⋅ ⋅= ⋅ ⋅= ⋅ ⋅=

simple interest principal rate time$200 8% 2$200 0.08 2$32

2. = ⋅ ⋅= ⋅ ⋅= ⋅ ⋅=

simple interest principal rate time$800 9% 3$800 0.09 3$216

3. = ⋅ ⋅= ⋅ ⋅= ⋅ ⋅=

simple interest principal rate time$160 11.5% 4$160 0.115 4$73.60

4. = ⋅ ⋅= ⋅ ⋅= ⋅ ⋅=

simple interest principal rate time$950 12.5% 5$950 0.125 5$593.75

5. simple interest principal rate time1$5000 10% 12

$5000 0.10 1.5$750

= ⋅ ⋅

= ⋅ ⋅

= ⋅ ⋅=



379

6. = ⋅ ⋅

= ⋅ ⋅

= ⋅ ⋅=

simple interest principal rate time1

$1500 14% 24

$1500 0.14 2.25$472.50

7. = ⋅ ⋅

= ⋅ ⋅

= ⋅ ⋅=


$375 18%12

$375 0.18 0.5$33.75

8. = ⋅ ⋅

= ⋅ ⋅

= ⋅ ⋅

=


$775 15%122

$775 0.153

$77.50

9. simple interest principal rate time21$2500 16%12

$2500 0.16 1.75$700

= ⋅ ⋅

= ⋅ ⋅

= ⋅ ⋅=

10. = ⋅ ⋅

= ⋅ ⋅

= ⋅ ⋅=


$1000 10%12

$1000 0.10 1.5$150

11. = ⋅ ⋅= ⋅ ⋅= ⋅ ⋅=

simple interest principal rate time$162,500 12.5% 5$162,500 0.125 5$101,562.50

The amount of interest is $101,562.50.

12. = ⋅ ⋅= ⋅ ⋅= ⋅ ⋅=

simple interest principal rate time$265,000 8.25% 30$265,000 0.0825 30$655,875

The amount of interest is $655,875.

13. simple interest principal rate time15$5000 9%12

$5000 0.09 1.25$562.50

= ⋅ ⋅

= ⋅ ⋅

= ⋅ ⋅=

Total = $5000 + $562.50 = $5562.50

14. = ⋅ ⋅

= ⋅ ⋅

= ⋅ ⋅=


$4500 14%12

$4500 0.14 0.75$472.50

= + =Total amount $4500 $472.50 $4972.50

15. = ⋅ ⋅= ⋅ ⋅= ⋅ ⋅=

Simple interest principal rate time$8500 17% 4$8500 0.17 4$5780

= + =Total amount $8500 $5780 $14,280

16. = ⋅ ⋅= ⋅ ⋅= ⋅ ⋅=

Simple interest principal rate time$2000 8% 5$2000 0.08 5$800

= + =Total amount $2000 $800 $2800

17. ⋅

⋅

⎛ ⎞= +⎜ ⎟⎝ ⎠

⎛ ⎞= +⎜ ⎟⎝ ⎠

=≈

2 15

30

1

0.146150 1

2

6150(1.07)46,815.37

n tr

A Pn

The total amount is $46,815.37.

18. ⋅

⋅

⎛ ⎞= +⎜ ⎟⎝ ⎠

⎛ ⎞= +⎜ ⎟⎝ ⎠

=≈

110

10

1

0.152060 1

1

2060(1.015)2390.71

n tr

A Pn

The total amount is $239.71.

19. ⋅

⋅

⎛ ⎞= +⎜ ⎟⎝ ⎠

⎛ ⎞= +⎜ ⎟⎝ ⎠

⎛ ⎞= +⎜ ⎟⎝ ⎠

≈

365 5

1825

1

0.081560 1

365

0.081560 1

3652327.14

n tr

A Pn




380

20. ⋅

⋅

⎛ ⎞= +⎜ ⎟⎝ ⎠

⎛ ⎞= +⎜ ⎟⎝ ⎠

=≈

4 15

60

1

0.101450 1

4

1450(1.025)6379.70

n tr

A Pn


21. ⋅

⋅

⎛ ⎞= +⎜ ⎟⎝ ⎠

⎛ ⎞= +⎜ ⎟⎝ ⎠

=≈

2 20

40

1

0.0910,000 1

2

10,000(1.045)58,163.65

n tr

A Pn


22. ⋅

⋅

⎛ ⎞= +⎜ ⎟⎝ ⎠

⎛ ⎞= +⎜ ⎟⎝ ⎠

⎛ ⎞= +⎜ ⎟⎝ ⎠

≈

365 10

3650

1

0.083500 1

365

0.083500 1

365$7788.71

n tr

A Pn


23. ⋅

⋅

⎛ ⎞= +⎜ ⎟⎝ ⎠

⎛ ⎞= +⎜ ⎟⎝ ⎠

==

11

1

0.092675 1

12675(1.09)2915.75

n tr

A Pn


24. ⋅

⋅

⎛ ⎞= +⎜ ⎟⎝ ⎠

⎛ ⎞= +⎜ ⎟⎝ ⎠

=≈

2 1

2

1

0.106375 1

2

6375(1.05)7028.44

n tr

A Pn


25. ⋅

⋅

⎛ ⎞= +⎜ ⎟⎝ ⎠

⎛ ⎞= +⎜ ⎟⎝ ⎠

=≈

1 5

5

1

0.082000 1

1

2000(1.08)2938.66

n tr

A Pn


26. ⋅

⋅

⎛ ⎞= +⎜ ⎟⎝ ⎠

⎛ ⎞= +⎜ ⎟⎝ ⎠

=≈

2 5

10

1

0.082000 1

2

2000(1.04)2960.49

n tr

A Pn


27. ⋅

⋅

⎛ ⎞= +⎜ ⎟⎝ ⎠

⎛ ⎞= +⎜ ⎟⎝ ⎠

=≈

4 5

20

1

0.082000 1

4

2000(1.02)2971.89

n tr

A Pn


28. ⋅

⋅

⎛ ⎞= +⎜ ⎟⎝ ⎠

⎛ ⎞= +⎜ ⎟⎝ ⎠

⎛ ⎞= +⎜ ⎟⎝ ⎠

≈

365 5

1825

1

0.082000 1

365

0.082000 1

3652983.52

n tr

A Pn


29. perimeter = 10 + 6 + 10 + 6 = 32 The perimeter is 32 yards.

30. Perimeter = 18 + 16 + 12 = 46 The perimeter is 46 centimeters.

31. Perimeter = 7 + 7 + 7 + 7 + 7 = 35 The perimeter is 35 meters.

32. Perimeter = 21 + 21 + 21 + 21 = 84 The perimeter is 84 miles.

33. + = ⋅ + ⋅ = + =5 4 5 4 9

4 5 4 5 5 4 20 20 20

x x x x x x x



381

34. ⋅⎛ ⎞ ⎛ ⎞− ÷ − = − ⋅ − = =⎜ ⎟ ⎜ ⎟ ⋅⎝ ⎠ ⎝ ⎠

5 5 5

4 5 4 4 4

x x x x

x x

35. ⎛ ⎞⎛ ⎞ ⎛ ⎞⎛ ⎞− − = − −⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠ ⎝ ⎠⎝ ⎠

= − ⋅ − ⋅

= − −

= −

= −

2 1 9 2 2 18

3 3 10 5 9 502 50 18 9

9 50 50 9100 162

450 450262

450131

225

36. ⋅ ⋅ ⋅

÷ ⋅ = ⋅ ⋅ = =⋅ ⋅

3 9 1 3 22 1 3 2 11 1 2

11 22 3 11 9 3 11 9 3 9




Chapter 7 Vocabulary Check

1. In a mathematical statement, of usually means “multiplication.”

2. In a mathematical statement, is means “equals.”

3. Percent means “per hundred.”

4. Compound interest is computed not only on the principal, but also on interest already earned in previous compounding periods.

5. In the percent proportion amount

base =

percent.

100

6. To write a decimal or fraction as a percent, multiply by 100%.

7. The decimal equivalent of the % symbol is 0.01.

8. The fraction equivalent of the % symbol is 1

.100

9. The percent equation is base ⋅ percent = amount.

10. Percent of decrease = amount of decrease

.original amount

11. Percent of increase = amount of increase

.original amount

12. Sales tax = tax rate ⋅ purchase price.

13. Total price = purchase price + sales tax.

14. Commission = commission rate ⋅ sales.

15. Amount of discount = discount rate ⋅ original price.

16. Sale price = original price − amount of discount.

Chapter 7 Review

1. =37

37%100

37% of adults preferred pepperoni.

2. =77

77%100

77% of free throws were made.

3. 26% = 26(0.01) = 0.26

4. 75% = 75(0.01) = 0.75

5. 3.5% = 3.5(0.01) = 0.035

6. 1.5% = 1.5(0.01) = 0.015

7. 275% = 275(0.01) = 2.75

8. 400% = 400(0.01) = 4.00 or 4

9. 47.85% = 47.85(0.01) = 0.4785

10. 85.34% = 85.34(0.01) = 0.8534

11. 1.6 = 1.6(100%) = 160%

12. 0.055 = 0.055(100%) = 5.5%

13. 0.076 = 0.076(100%) = 7.6%

14. 0.085 = 0.085(100%) = 8.5%

15. 0.71 = 0.71(100%) = 71%

16. 0.65 = 0.65(100%) = 65%

17. 6 = 6(100)% = 600%

18. 9 = 9(100%) = 900%



382

19. ⎛ ⎞= =⎜ ⎟⎝ ⎠

1 77% 7

100 100

20. ⎛ ⎞= = =⎜ ⎟⎝ ⎠

1 15 315% 15

100 100 20

21. ⎛ ⎞= = =⎜ ⎟⎝ ⎠

1 25 125% 25

100 100 4

22. ⎛ ⎞= ⎜ ⎟⎝ ⎠

=

⋅=

⋅

=

=

18.5% 8.5

1008.5

1008.5 10

100 1085

100017

200

23. ⎛ ⎞= ⎜ ⎟⎝ ⎠

=

⋅=

⋅

=

=

110.2% 10.2

10010.2

10010.2 10

100 10102

100051

500

24. ⎛ ⎞= = = =⎜ ⎟⎝ ⎠

2 50 50 1 50 116 % %

3 3 3 100 300 6

25. ⎛ ⎞= = = =⎜ ⎟⎝ ⎠

1 100 100 1 100 133 % %

3 3 3 100 300 3

26. ⎛ ⎞= = = =⎜ ⎟⎝ ⎠

1 110 10 1110% 110 1 1

100 100 100 10

27. = ⋅ = =2 2 100 200

% % 40%5 5 1 5

28. = ⋅ = =7 7 100 700

% % 70%10 10 1 10

29. = ⋅ = = =7 7 100 700 175 1

% % % 58 %12 12 1 12 3 3

30. = ⋅ = =2 5 100 500 2

1 % % 166 %3 3 1 3 3

31. = ⋅ = =1 5 100 500

1 % % 125%4 4 1 4

32. = ⋅ = =3 3 100 300

% % 60%5 5 1 5

33. = ⋅ = =1 1 100 100

% % 6.25%16 16 1 16

34. = ⋅ = =5 5 100 500

% % 62.5%8 8 1 8

35. = ⋅=

=

=

1250 1.25%1250 0.0125

1250 0.0125

0.0125 0.0125100,000

xxx

x

1250 is 1.25% of 100,000.

36. = ⋅

= ⋅ ⋅

= ⋅

=

133 % 24,000

3100 1

24,0003 100

124,000

38000

x

x

x

x

8000 is 1

33 %3

of 24,000.

37. = ⋅

=

==

124.2 540124.2 540

540 5400.2323%

xx

xx

124.2 is 23% of 540.

38. = ⋅= ⋅

=

=

22.9 20%22.9 0.2022.9 0.20

0.20 0.20114.50

xx

x

x

22.9 is 20% of 114.50.

39. x = 17% ⋅ 640 x = 0.17 ⋅ 640 x = 108.8 108.8 is 17% of 640.



383

40. = ⋅

=

==

693 462693 462

462 4621.5

150%

xx

xx

693 is 150% of 462.

41. =

⋅ = ⋅=

=

=

104.5 25

100104.5 100 25

10, 450 2510, 450 25

25 25418

bb

bb

b

104.5 is 25% of 418.

42. =

⋅ = ⋅=

=

=

16.5 5.5

10016.5 100 5.5

1650 5.51650 5.5

5.5 5.5300

bb

bb

b

16.5 is 5.5% of 300.

43. =

⋅ = ⋅=

=

=

30

532 100100 30 532

100 15,960100 15,960

100 100159.6

a

aaa

a

159.6 is 30% of 532.

44. =

⋅ = ⋅=

=

=

63

35 10063 100 35

6300 356300 35

35 35180

p

ppp

p

63 is 180% of 35.

45. =

⋅ = ⋅=

=

=

93.5

85 10093.5 100 85

9350 859350 85

85 85110

p

ppp

p

93.5 is 110% of 85.

46. =

⋅ = ⋅=

=

=

33

500 100100 33 500

100 16,500100 16,500

100 100165

a

aaa

a

165 is 33% of 500.


= ⋅

=

==

1320 20001320 2000

2000 20000.6666%

xx

xx

66% of people own microwaves. Method 2:

=

⋅ = ⋅=

=

=

1320

2000 1001320 100 2000

132,000 2000132,000 2000

2000 200066

p

ppp

p

66% of people own microwaves.

48. 2000 is what percent of 12,360? Method 1:

= ⋅

=

≈≈

2000 12,3602000 12,360

12,360 12,3600.1616%

xx

xx

16% of freshmen are enrolled in prealgebra. Method 2:

=

⋅ = ⋅=

=

≈

200

12,360 1002000 100 12,360

200,000 12,360200,000 12,360

12,360 12,36016

p

ppp

p

16% of freshman are enrolled in prealgebra.



384

49. =

−=

=

≈≈



675141

6750.20920.9%

Violent crime decreased 20.9%.

50. =

−=

=

==



1617

161.0625106.25%

The charge will increase 106.25%.

51. = ⋅= ⋅= ⋅=

Amount of decreasepercent decrease original amount4% $215,0000.04 $215,000$8600

Total amount = $215,000 − $8600 = $206,400 $206,400 is expected to be collected next year.

52. Amount of increase = percent increase ⋅ original amount = 15% ⋅ $11.50 = 0.15 ⋅ $11.50 ≈ $1.73 Total amount = $11.50 + $1.73 = $13.23 The new hourly rate is $13.23.

53. = ⋅= ⋅= ⋅=

sales tax tax rate purchase price5.5% $2500.055 $250$13.75

Total amount = $250 + $13.75 = $263.75 The total price for the coat is $263.75.

54. = ⋅= ⋅= ⋅≈

sales tax tax rate purchase price4.5% $25.500.045 $25.50$1.15

The sales tax is $1.15.

55. = ⋅= ⋅= ⋅=

commission commission rate sales5% $100,0000.05 $100,000$5000

His commission is $5000.

56. = ⋅= ⋅= ⋅≈

commission commission rate sales7.5% $40050.075 $4005$300.38

Her commission is $300.38.

57. = ⋅= ⋅= ⋅=

Amount of discount discount original price30% $30000.30 $3000$900

Sale price = $3000 − $900 = $2100 The amount of discount is $900; the sale price is $2100.

58. = ⋅= ⋅= ⋅=

Amount of discount discount original price10% $900.10 $90$9.00

Sale price = $90 − $9 = $81 The amount of discount is $9; the sale price is $81.

59. = ⋅ ⋅

= ⋅ ⋅

= ⋅ ⋅

=

4$4000 12%

121

$4000 0.123

$160

I P R T

The simple interest is $160.

60. = ⋅ ⋅

= ⋅ ⋅

= ⋅ ⋅=

3$650 20%

12$6500 0.20 0.25$325

I P R T

The simple interest is $325.

61. ⋅

⋅

⎛ ⎞= +⎜ ⎟⎝ ⎠

⎛ ⎞= +⎜ ⎟⎝ ⎠

=≈

115

15

1

0.125500 1

1

5500(1.12)30,104.61

n tr

A Pn




385

62. ⋅

⋅

⎛ ⎞= +⎜ ⎟⎝ ⎠

⎛ ⎞= +⎜ ⎟⎝ ⎠

=≈

2 10

20

1

0.116000 1

2

6000(1.055)17,506.54

n tr

A Pn


63. ⋅

⋅

⎛ ⎞= +⎜ ⎟⎝ ⎠

⎛ ⎞= +⎜ ⎟⎝ ⎠

=≈

4 5

20

1

0.12100 1

4

100(1.03)180.61

n tr

A Pn


64. ⋅

⋅

⎛ ⎞= +⎜ ⎟⎝ ⎠

⎛ ⎞= +⎜ ⎟⎝ ⎠

=≈

4 20

80

1

0.181000 1

4

1000(1.045)33,830.10

n tr

A Pn


65. 3.8% = 3.8(0.01) = 0.038

66. 124.5% = 124.5(0.01) = 1.245

67. 0.54 = 0.54(100%) = 54%

68. 95.2 = 95.2(100%) = 9520%

69. ⎛ ⎞= =⎜ ⎟⎝ ⎠

1 4747% 47

100 100

70. ⎛ ⎞= ⎜ ⎟⎝ ⎠

=

⋅=

⋅

=

=

15.6% 5.6

1005.6

1005.6 10

100 1056

10007

125

71. = ⋅ = =3 3 100 300 1

% % 37 %8 8 1 8 2

72. = ⋅ = =6 6 100 600

% % 120%5 5 1 5

73. = ⋅=

=

=

43 16%43 0.16

43 0.16

0.16 0.16268.75

xxx

x

43 is 16% of 268.75.

74. = ⋅

=

==

27.5 2527.5 25

25 251.1

110%

xx

xx

27.5 is 110% of 25.

75. x = 36% ⋅ 1968 x = 0.36 ⋅ 1968 x = 708.48 708.48 is 36% of 1968.

76. = ⋅

=

==

67 5067 50

50 501.34

134%

xx

xx

67 is 134% of 50.

77. =

⋅ = ⋅=

=

=

75

25 10075 100 25

7500 257500 25

25 25300

p

ppp

p

75 is 300% of 25.

78. =

⋅ = ⋅=

=

=

16

240 100100 16 240

100 3840100 3840

100 10038.4

a

aaa

a

38.4 is 16% of 240.



386

79. =

⋅ = ⋅=

=

=

28 5

10028 100 5

2800 52800 5

5 5560

bb

bb

b

28 is 5% of 560.

80. =

⋅ = ⋅=

=

=

52

16 10052 100 16

5200 165200 16

16 16325

p

ppp

p

52 is 325% of 16.

81. = =78

0.26 26%300

26% of the soft drinks have been sold.

82. $96,950 ⋅ 7% = $96,950 ⋅ 0.07 = $6786.50 The house has lost $6786.50 in value.

83. = ⋅= ⋅=

Sales tax 8.75% $5680.0875 $568$49.70

Total price = $568 + $49.70 = $617.70 The total price is $617.70.

84. = ⋅= ⋅=

Amount of discount 15% $23.000.15 $23.00$3.45

85. = ⋅= ⋅

=

==

commission commission rate sales$1.60 $12.80

$1.60

$12.800.125

12.5%

r

r

rr

His rate of commission is 12.5%.

86. = ⋅ ⋅

= ⋅ ⋅

= ⋅ ⋅=

Simple interest principal rate time6

$1400 13%12

$1400 0.13 0.5$91

Total amount = $1400 + $91 = $1491 The total amount is $1491.

87. = ⋅ ⋅= ⋅ ⋅= ⋅ ⋅=

Simple interest principal rate time$5500 12.5% 9$5500 0.125 9$6187.50

Total amount = $5500 + $6187.50 = $11,687.50 The total amount is $11,687.50.

Chapter 7 Test

1. 85% = 85(0.01) = 0.85

2. 500% = 500(0.01) = 5

3. 0.6% = 0.6(0.01) = 0.006

4. 0.056 = 0.056(100%) = 5.6%

5. 6.1 = 6.1(100%) = 610%

6. 0.35 = 0.35(100%) = 35%

7. ⎛ ⎞= = =⎜ ⎟⎝ ⎠

1 120 1120% 120 1

100 100 5

8. ⎛ ⎞= = = =⎜ ⎟⎝ ⎠

1 38.5 385 7738.5% 38.5

100 100 1000 200

9. 1 0.2 2 10.2% 0.2

100 100 1000 500⎛ ⎞= = = =⎜ ⎟⎝ ⎠

10. = ⋅ = =11 11 100 1100

% % 55%20 20 1 20

11. = ⋅ = =3 3 100 300

% % 37.5%8 8 1 8

12. = ⋅ = =3 7 100 700

1 % % 175%4 4 1 4

13. = ⋅ = =1 1 100 100

% % 20%5 5 1 5

14. ⎛ ⎞= = =⎜ ⎟⎝ ⎠

1 64 1664% 64

100 100 25

15. Method 1: x = 42% ⋅ 80 x = 0.42 ⋅ 80 x = 33.6 33.6 is 42% of 80.



387

Method 2:

=

⋅ = ⋅=

=

=

42

80 100100 42 80

100 3360100 3360

100 10033.6

a

aaa

a

33.6 is 42% of 80.

16. Method 1: ⋅ =

=

=

=

0.6% 7.50.006 7.50.006 7.5

0.006 0.0061250

xxx

x

0.6% of 1250 is 7.5. Method 2:

=

⋅ = ⋅=

=

=

7.5 0.6

1007.5 100 0.6

750 0.6750 0.6

0.6 0.61250

bb

bb

b

0.6% of 1250 is 7.5.

17. Method 1: = ⋅

⋅=

==

567 756567 756

756 7560.7575%

xx

xx

567 is 75% of 756. Method 2:

=

⋅ = ⋅=

=

=

567

756 100567 100 756

56,700 75656,700 756

756 75675

p

ppp

p

567 is 75% of 756.

18. 12% of 320 is what number? ⋅ =⋅ =

=

12% 3200.12 320

38.4

xxx

There are 38.4 pounds of copper.

19. 20% of what number is $11,350? ⋅ =

=

=

=

20% $11,3500.20 $11,3500.2 $11,350

0.2 0.2$56, 750

xxx

x

The value of the potential crop is $56,750.

20. tax = 1.25% ⋅ $354 = 0.0125 ⋅ $354 ≈ $4.43 total amount = $354 + $4.43 = $358.43 The total amount of the stereo is $358.43.

21. =

−=

=

=


original amount26, 460 25,200

25,2001260

25,2000.05

The increase in population was 5%.

22. = ⋅= ⋅=

Amount of discount 15% $1200.15 $120$18

Sale price = $120 − $18 = $102 The amount of the discount is $18; the sale price is $102.

23. = ⋅= ⋅=

commission 4% $98750.04 $9875$395

His commission was $395.

24. = ⋅

=

≈≈

$1.53 rate $152.99$1.53

$152.990.011%

r

rr


25. = ⋅ ⋅

= ⋅ ⋅

= ⋅ ⋅=


$2000 9.25% 32

$2000 0.0925 3.5$647.5



388

26. ⋅

⋅

⎛ ⎞= +⎜ ⎟⎝ ⎠

⎛ ⎞= +⎜ ⎟⎝ ⎠

=≈

1 5

5

1

0.081365 1

1

1365(1.08)2005.63

n tr

A Pn

The total amount of $2005.63.

27. = ⋅ ⋅

= ⋅ ⋅

= ⋅ ⋅=

Simple interest principal rate time6

$400 13.5%12

$400 0.135 0.5$27

Total amount = $400 + $27 = $427

28. =

−=

=

≈≈



125,5877241

125,5870.05765.8%

The number of crimes has decreased 5.8%.

Cumulative Review Chapters 1−7

1. ×

23686

1 41618 880

20,296

2. ×

40976

2 45428 630

31,084

3. −3 − 7 = −3 + (−7) = −10

4. 8 − (−2) = 8 + 2 = 10

5. − = −− + = − +

=

2 12 2 1 2

1

xx

x

6. + =+ − = −

= −

4 34 4 3 4

1

xx

x

7. − + =⋅ − ⋅ + =

− + =− =

− + = +=

=

=

3(2 6) 6 03 2 3 6 6 0

6 18 6 06 12 0

6 12 12 0 126 126 12

6 62

xx

xx

xxx

x

8. − =⋅ − ⋅ =

− =− − = −

− = −− −

=− −

=

5( 2) 35 5 2 3

5 10 35 5 10 3 5

10 210 2

2 25

x xx x

x xx x x x

xx

x

9. ⋅

= ⋅ = =⋅

3 7 3 7 213

1 7 1 7 7

10. ⋅

= ⋅ = =⋅

8 5 8 5 408

1 5 1 5 5

11. ⋅

− = −⋅ ⋅

10 2 5

27 3 3 3

Since 10 and 27 have no common factors, −10

27

is already in simplest form.

12. ⋅ ⋅

= =⋅

10 5 2 5

32 16 2 16

y y y

13. ⋅

− ÷ − = − ⋅− = =⋅ ⋅

5 3 5 4 5 4 5

16 4 16 3 4 4 3 12

14. − ⋅ ⋅

÷ = − ⋅ = − = −⋅

2 7 2 10 2 2 5 4

5 10 5 7 5 7 7

15. ⎛ ⎞− = − − − = − + = − = −⎜ ⎟⎝ ⎠

8 3 8 3 5 1

10 10 10 10 10 2y x

16. − −⎛ ⎞ ⎛ ⎞+ = + = + =⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠

2 1 4 3 12 3 2 3

5 5 5 5 5x y



389

17. − − + = − ⋅ − ⋅ + ⋅

= − − +

=

3 1 6 3 7 1 2 6 4

4 14 7 4 7 14 2 7 421 2 24

28 28 281

28

18. + − = ⋅ + ⋅ − ⋅

= + −

=

2 7 1 2 5 7 3 1 15

9 15 3 9 5 15 3 3 1510 21 15

45 45 4516

45

19.

+ ⋅ +=

− ⋅ − ⋅

+=

−

=

= ÷

= ⋅

⋅ ⋅=

⋅ ⋅

=

3 31 1 42 8 2 4 83 3 31 1 24 6 4 3 6 2

348 89 2

12 12787

127 7

8 127 12

8 77 4 3

4 2 73

2

20.

+ ⋅ +=

− ⋅ − ⋅

+=

−

=

= ÷

= ⋅

⋅ ⋅=

⋅ ⋅

=

2 1 2 2 13 6 3 2 63 3 3 5 3 44 5 4 5 5 4

4 16 6

15 1220 20563

205 3

6 205 20

6 35 2 10

2 3 350

9

21. = +

⎛ ⎞ ⎛ ⎞= +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

= ⋅ + ⋅

= +− = + −

=

1

2 3 21

6 62 3 2

13 6 6

3 23 2 3

3 2 2 3 23

x x

x x

xx

x xx x x x

x

22.

+ = −

⎛ ⎞ ⎛ ⎞+ = −⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

⋅ + ⋅ = ⋅ − ⋅

+ = −+ + = − +

+ =+ − = −

=

=

=

13

2 5 51

10 10 32 5 5

110 10 10 3 10

2 5 55 2 30 2

5 2 2 30 2 27 2 30

7 2 2 30 27 287 28

7 74

x x

x x

x x

x xx x x x

xx

xx

x

23. a. ⋅ + +

= = =2 9 4 2 36 2 38

49 9 9 9

b. ⋅ + +

= = =8 11 1 8 11 8 19

111 11 11 11

24. a. ⋅ + +

= = =2 5 3 2 15 2 17

35 5 5 5

b. ⋅ + +

= = =2 7 6 2 42 2 44

67 7 7 7

25. = =125 1

0.1251000 8

26. = =85 17

0.85100 20

27. − = −83

105.083 1051000

28. = =15 3

17.015 17 171000 200



390

29. −

85.0017.31

67.69

30. −

38.0010.06

27.94

31. 7.68 × 10 = 76.8

32. 12.483 × 100 = 1248.3

33. (−76.3)(1000) = −76,300

34. −853.75 × 10 = −8537.5

35. x ÷ y = 2.5 ÷ 0.05

0.05 2.5 becomes −

505 250

2500

36. =

=

4.75100470

4.75100

4.7 4.75 False

x

�

No, 470 is not a solution.

37. 55, 67, 75, 86, 91, 91 +

= = =75 86 161

median 80.52 2

38. + + +

= = =36 40 86 30 192

mean 484 4

39. = =2.5 2500 50

3.15 3150 63

40. = =5.8 58 29

7.6 76 38

41. −

−

0.2116 3.36

32

1616

0

The unit price is $0.21/ounce.

42. −

−

−

2.2540 90.00

8010 0

8 0

2 002 00

0

The price is $2.25 per tile, or $2.25 per square foot.

43.

≠

4.1 2.9

7 54.1(5) 2.9(7)

20.5 20.3

�

�

No, it is not a true proportion.

44.

=

6.3 3.5

9 56.3(5) 3.5(9)

31.5 31.5

�

�

Yes, it is a true proportion.

45. =

⋅ = ⋅=

=

=

5 miles miles

2 inches 7 inches5 7 235 235 2

2 217.5

x

xxx

x

17.5 miles corresponds to 7 inches.

46. =

⋅ = ⋅=

=

=

7 problems problems

6 minutes 30 minutes7 30 6210 6210 6

6 635

x

xxx

x

The student can complete 35 problems in 30 minutes.

47. ⎛ ⎞= = =⎜ ⎟⎝ ⎠

1 1.9 191.9% 1.9

100 100 1000

48. ⎛ ⎞= = =⎜ ⎟⎝ ⎠

1 2.3 232.3% 2.3

100 100 1000

49. ⎛ ⎞= = =⎜ ⎟⎝ ⎠

1 100 1 100 133 %

3 3 100 300 3

50. ⎛ ⎞= = =⎜ ⎟⎝ ⎠

1 108 2108% 108 1

100 100 25


Date post:	25-Apr-2018
Category:	Documents
Upload:	doanliem
View:	224 times
Download:	4 times

Chapter 7 11 25 40 25 11. 40 = ... 23. 18 422 8% 8 100 100 4 25 25 ... Chapter 7: Percent ISM:...

Documents