SOLUTIONS MANUAL - EIGHTH E DITION Robert Blitzer Part 2: Ch 8-14:...

SOLUTIONS MANUAL

D

ANIEL S. MILLER

T

HINKING MATHEM ATICALLY

EIGHTH E

DITION

Robert Blitzer Part 2: Ch 8-14: Page 2-343 Part 1: Ch 1-7: Page 344-721 1 / 4

Chapter 8 Personal Finance Copyright © 2024 Pearson Education Ltd. 379 Checkpoints 8.1

1.Step 1: 1

1 8 0.125

8

=  =

Step 2: 0.125 100 12.5=

Step 3: 12.5%

2.0.023 2.3%=

3.a. 67% 0.67= b.250% 2.50 2.5== 4.a. 6% of $1260 0.06 $1260 $75.60=  = The tax paid is $75.60 b.$1260.00 $75.60 $1335.60+= The total cost is $1335.60 5.a. 35% of $380 0.35 $380 $133=  = The discount is $133 b.$380 $133 $247−= The sale price is $247 6.a. Percent of increase =amount of increase original amount 22 33 4

0.66 66 %

6 = = = b.Percent of decrease =amount of decrease original amount 4

0.4 40%

10 = = =

7.Amount of decrease: $940 $611 $329−= amount of decrease $329

0.35 35%

original amount $940 = = = There was a 35% decrease in price.

8.Amount of increase: 12% 10% 2%−= amount of increase 2%

0.2 20%

original amount 10% = = = There was a 20% increase for this episode.

9.a. 20% of $1200 0.20 $1200 $240=  = Taxes for year 1 are $1200 $240 $960−= 20% of $960 0.20 $960 $192=  = Taxes for year 2 are $960 $192 $1152+=

• $1200 $1152 $48

0.04 4%

$1200 $1200

− = = = Taxes for year 2 are 4% less than the original amount.Concept and Vocabulary Check 8.1

C1. 100

C2. 7; 8; 100; a percent sign C3. two; right; a percent sign C4. two; left; a percent sign C5. tax rate; item’s cost C6. discount rate; original price C7. the amount of increase; the original amount C8. the amount of decrease; the original amount C9. false; Changes to make the statement true will vary.

A sample change is: Only 6 reindeer remain.

C10. false; Changes to make the statement true will vary.

A sample change is: You spent $500 on gifts.

Exercise Set 8.1

• 2

2 5 0.4 40%

5

=  = =

• 3

3 5 0.6 60%

5

=  = = 9

9 10 0.9 90%

10

• 3

3 4 0.75 75%

4

=  = = 3

3 6 0.5 50%

6 2 / 4

Chapter 8 Personal Finance 380 Copyright © 2024 Pearson Education Ltd.

• 7

7 8 0.875 87.5%

8

=  = =

• 1

1 40 0.025 2.5%

40

=  = =

• 3

3 40 0.075 7.5%

40

=  = =

• 9

9 80 0.1125 11.25%

80

=  = =

10. 13

13 80 0.1625 16.25%

80

=  = =

11. 0.59 = 59%

12. 0.96 = 96%

13. 0.3844 = 38.44%

14. 0.003 = 0.3%

15. 2.87 = 287%

16. 9.83 = 983%

17. 14.87 = 1487%

18. 19.63 = 1963%

19. 100 = 10,000%

20. 95 = 9500%

21. 72% = 0.72

22. 38% = 0.38

23. 43.6% = 0.436

24. 6.25% = 0.0625

25. 130% = 1.3

26. 260% = 2.6

27. 2% = 0.02

28. 6% = 0.06

• 1

% 0.5% 0.005

2 ==

• 3

% 0.75% 0.0075

4 ==

• 5

% 0.625% 0.00625

8 ==

• 1

% 0.125% 0.00125

8 ==

• 1

62 % 62.5% 0.625

2 ==

• 1

87 % 87.5% 0.875

2 ==

35. A PB= 0.03 200

6 A A = =

36. A PB= 0.08 300

24 A A = =

37. A PB= 0.18 40

7.2 A A = =

38. A PB= 0.16 90

14.4 A A = =

39. A PB= 3 0.60

3 0.60

0.60 0.60

5 B B B = = =

40. A PB= 8 0.40

8 0.40

0.40 0.40

20 B B B = = =

41. A PB= 40.8 0.24

40.8 0.24

0.24 0.24

170 B B B = = =

42. A PB= 51.2 0.32

51.2 0.32

0.32 0.32

160 B B B = = =

• / 4

Section 8.1 Percent, Sales Tax, and Discounts Copyright © 2024 Pearson Education Ltd. 381

43. A PB= 3 15

• 15

15 15 0.2 20% P P P P =  = = =

44. A PB= 18 90

18 90 90 90 0.2 20% P P P P =  = = =

45. A PB= 0.3 2.5

0.3 2.5

2.5 2.5

0.12 12% P P P P =  = = =

46. A PB= 0.6 7.5

0.6 7.5

7.5 7.5

0.08 8% P P P P =  = = =

• a. (0.06)(32,800) = $1968
• 32,800 + 1968 = $34,768
• a. (0.07)(96) = $6.72
• 96 + 6.72 = $102.72
• a. (0.12)(860) = $103.20
• 860 – 103.20 = $756.80
• a. (0.40)(16.50) = $6.60
• 16.50 – 6.60 = $9.90

51. 70

0.192 19.2%

365 =

52. 37

0.101 10.1%

365 =

53. 71 25 46

1.84 184%

25 25 − = = =

54. 61 25 36

1.44 144%

25 25 − = = =

55. 840 714

0.15 15%

840 − ==

56. 380 266

0.30 30%

380 − ==

• Amount after first year

= 10,000 – (0.3)(10,000)

= $7000

Amount after second year

= 7000 + (0.4)(7000)

= $9800

Your adviser is not using percentages properly.

Actual change: 10,000 9800

0.02 2%

10,000

− == loss.

• The salesman is misusing percentages. 100% 30% 70%−=

20% of 70% 0.70(0.20) 0.14 14%= = = Percent reduction 30% 14% 44%= + =

• - 64. Answers will vary.
• does not make sense; Explanations will vary.

Sample explanation: 20% of $80 is $16. This will

make the total $96.

• does not make sense; Explanations will vary.

Sample explanation: A price can not drop more than

100%.

• does not make sense; Explanations will vary.

Sample explanation: Since 1.01 1.01 1.0201= the

percent of increase is 2.01%.

• does not make sense; Explanations will vary.

Sample explanation: The increase is 30% 20% 10% 1

0.5 50%

20% 20% 2

−

= = = =

.

• First, find the discount amount. 15% $720 0.15 $720 $108 =  =

Next, find the sales price. $720 $108 $612−=

Then, find the tax. 6% $612 0.06 $612 $36.72 =  =

Finally, find the total cost. $612 $36.72 $648.72+= Percent reduction 30% 14% 44%= + =

• / 4