=171K

3.1 Solving Literal Equations

1. x = a b

2. x = nq

3. x = r2

4. x = 3 m

5. b = y – mx

6. x = b – d

7. t = I Pr

8. c = p – a – b

9. t = d r

10. r =

2

c

π

11. s =

3

p

12. h = V₂ r

π

13. P = 14

3

r x

15. x = y b m

−

16. x = ae + a

17. x₁ = mx2 y1 y2 m

+ −

18. P₂ = 1 1 2 1 2 PV T

TV

19. H =

2 2 2 S r r π π −

20. y = c ax b

−

21. x = – 2

b

22. y =

2

x a

−

23. n = bx x −b

24. x = r

q− Pn or

r Pn q

− −

25. v = df di t

−

; v = 88 ft/sec 26. H = 3V₂

r

π ; H = 24 cm

27. h = S cr c

−

Section 3.1

28. x₂ = y2 y1 mx1 m

− +

; x₂ = 2 29. x = bn

n b−

30. p =

2

mr q s r

+ −

31. b =

1

c c +

32. a =

2

c x + c − d

33. T₂ = 2 2 1 1 1 P V T

PV ; T2 = 171 K 34. m =

2

1 2

E

gh+ v

35–36.

Vehicle Gallons

Consumed Gallons Saved

Work van 1500

Mr. Hill

SUV 1154

346 gal

Compact

car 500

Mrs. Hill

Hybrid 250

250 gal

Old (d) m ÷ _d

General

Expressions _{New (n)}

m ÷ _n

Section 3.1

37. An expression represents a single quantity, while an equation states that two different expressions are equal.

38. F = ma

39. I = R – E

40. x = 1

5

41. y = 12 42. c = 5 43. s = 42 44. a7b–4

45. c–10d 6f –3

3.2 Ratios and Proportions

1. 4 to 5 2. 4 to 3 3. 1 to 3 4. 1 to 4

5. 17 points/game 6. $2.50/gal

7. $9.25/hr 8. 25 bu/acre 9. $18.25/yr 10. 25

¢

12. 27.7 m/sec 13. x = 56

14. y = 70

15. z = 1000

16. a = 36

25 = 1.44

17. b = 7

8 = 0.875

18. c = 128

7

≈ _18.3

Section 3.2

21. d = 9

22. y = 7

23. n = 9

24. p = –3

25. q = 1

2 = 0.5

26. r = 2

3 = 0.6

27. $1.33/roll

28. $1.91/roll

29. $18/shirt

30. $22.50/shirt

31. $190

32. 2.5 hr

33. 47 oz

34. 195 students

35. 18 volleyball players

36. 27 coils

37a. b s −b

37b. s b s

−

38. three-point shots

40. 7.20g/cm3

41a. 346 gal

41b. 250 gal

42. 152 gal

43. 4

9

44. –9

4

45. 25

49

46. x = –1.5 = –3

2

47. a = 135

48. x = 2n m

49. h = 2 440

11

w+

50. $2850

51. –1, 1, 3

3.3 Similar Figures and Scale Models

1. ∠_R ≅ ∠_Z, ∠_S ≅ ∠_{Q, and} ∠_B ≅ ∠_M;

RS ZQ =

SB QM =

BR MZ

2. 58°

3. x = 17.5 units; y = 20 units 4. a = 48 units; b = 54.4 units 5.

21 DEF p

= 15

6 ;

pDEF = 52.5 units

6.

42 XYZ p

= 32

10 ;

pXYZ = 134.4 units

7. 70 mi 8. 16 in.

9. 1 in. : 20 mi 10. 1 in. : 30 mi 11. 140 ft × _{230 ft}

12. 24 in. × _{10.6 in.}

13. 12 in. × _{8 in.}

14. 60 in. = 5 ft 15. 2.4 in.

16. 15.625 ft

18. DE = 3 units;

BC = 3.75 units 19. MNO

RTS A

A =

9

4; ARTS = 24 units 2

20

.

A =

9 16;

AABCDE = 24.75 units2

21. h = 20 units

22. s = 18 units; l = 10 units 23. S

L V

V =

8

125; VL = 3000 units 3

24. L S V

V =

27

8 ; VS = 16 units 3

25. 21.6 units and 26.4 units; 60 units

26. 6 : 5; 6 : 5 27. 4 : 25; 8 : 125 28. 3 : 2; 27 : 8 29. 147 ft2

30. 64 ft2 31. 160 ft 32. 5000 ft3

33. 1029π _units3

34. 24 in.

Section 3.3

36. 48 in. by 30 in. 37. 30 in.

38. Answers will vary. 39. 4.0 units

40. 4.9 units 41a. 3

130

41b. 1

60

41c. 1

99

42. The SUV option will save the most fuel, and the new sedan option will save the least.

49. – 7

12

50. 6 5

42

51. 47

60

52. –13

3.4 The Percent Equation

1. 0.69, 69

100

2. 1.87, 187

100

3. 0.75, 3

4

4. 0.14, 7

50

5. 25%, 1

4

6. 57%, 57

100

7. 350%, 7

2

8. 0.6, 60% 9. 7.5, 750% 10. 0.125, 12.5% 11. 126

12. 24% 13. 82.76 14. 712.8 15. 3

16. 2008% 17. 33,075 18. 65

19. 500 20. 53%

21. 40%; 60% 22. 144°

23. 236 24. $1500 25. $8.57/hr 26. 69%; yes 27. 85%

28. 70 games

29. $20.6 million

30. $2.94; $51.86; no 31. 33 – 46 lb

32. 12%; Athletes 33. 167.7 lb

34. 8% protein, 22% fat, and 70% carbohydrates; too

many carbohydrates and not enough protein

Section 3.4

36. 37% protein, 32% fat, and 31% carbohydrates; too much protein and not enough carbohydrates 37. 662,080 vehicles

38. 24%

39. 9,895,000 people

40. $3.50/lb; $3.33/lb; $3.42/lb

41.–43.

Mileage of Vehicle Replacing the Following

Work Van Old Sedan Compact Car

Producing the Same Savings as the Following

NA 30.8 97.5 SUV for work van

12 25.7 NA Hybrid for compact car

44. –15 45. 5 46. 1

48

47. 0.39 48. x = 21

4 = 5.25

49. x = 28

3 = 9.3

50. x = 7.5 in. 51. 99 in.2

52. x = 4

2

bd − dpq

53. x = 3c 2b ac

3.5 Percent Change and Error

1. 25% 2. 50% 3. 650% 4. 99.75% 5. 980

6. $34 7. 270 8. 1274 9. 1230 10. 315

11. 15; 10%

12. –0.1; 4% 13. 22.2% 14. 66.7%

15. 21.1% increase; 83 16. 6.8% decrease; 550 17. 115; 17.4% increase 18. 120; 27.5% decrease

19. subtract 39; 31.2% decrease 20. add 47; 28.8% increase

23. 1400; subtract 1050 24. 19.2; add 28.8

25. 1250; 1225 26. 0.24; 0.54 27. 3.3%

28. 1.3%

29. 0.13g/mL; 13% 30. –6.0°_{C; 7.7%}

31. 6.6% 32. 4.0% 33a. 24 33b. 16

34. No; 400% of x = 4x is the increase. The new number is x + 4x = 5x.

35. –30 (if the number

represents a quantity that can be negative; otherwise, it is not possible)

36. 125%

Section 3.5

38. The final is less than the original since the decrease is computed on a larger number than the increase. You are subtracting more than you added.

39. 20%

40. 1250 gal

41. Answers are given in terms of g, the current price per gallon.

41a. 104.17g

41b. 28.85g

41c. 20.83g

41d. 12.63g

42. x = 0.6 43. y = 7 44. z = 17

3

45. 105% 46. 6

47. 150

48. No; the sides are not proportional since 4

3

≠ 6 5.

49. 71

3

50. The Multiplication Property of Equality and the

3.6 Money

1. $4.00 2. $2.60 3. $13.00 4. $14.25 5. $4123 6. $132,050 7. 7%

8. $14,003.15 9. $12,579 10. 2.5% 11. $15; $90

12. 40%, $9.80 13. $120; $138 14. 35%; $9.11 15. $19.95; 24% 16. $23.10; $53.90 17. $6.75; 15% 18. 6%; $1800 19. $749; $501.83 20. 70%; $7.20 21. $300

23. $5000 24. 2.5%

25. $10.07; $66.00

26. J: $19.00, L: $15.50, and K: $12.75

27. $851 28. $87,500 29. 16% 30. $6630

31. $67.50; $33.75 32. $24; $45

33. $131.25; 81.25%

34. $29.90; 90%

35. $2500 at 5% and $7500 at 6%

36. $7500 at 6% and $6200 at 4%

37. $1800 for 9 mo and $2500 for 18 mo 38. $3500

39. $10,080 for 2.5 yr and $7000 for 3 yr

40. new car: $20,000; used car: $8500 41. 555

Section 3.6

42. 28 43. –6 44. 19

24

45. 197

48

46. –a2b + 2ab2

47. 2x2 – 3xy + 2y2

3.7 Motion

1. 54 2. 66 3.

19

d

4. 52t

5. 20

6. 35(r + 2) 7. r

8. 4 9. 7ab

10.

16

d

11. 125 mi 12. 6 hr

13. 400 mi/hr 14. 4 hr

15. 3

4 hr

Section 3.7

18. Frank: 12 mi/hr; Ted: 8 mi/hr

19. 6 hr

20. passenger train: 63 mi/hr; coal train: 40 mi/hr

21. up: 10 ft/sec; down: 80 ft/sec 22. 124.8 mi

23. 144 mi 24. 2 hr

25. 1 hr

26. Jay: 30r_{1 5} 220;

r_{1 5} 7.3 yd/sec Zeke: 30r_{2 5} 210;

r_{2 5} 7 yd/sec

Zeke’s time: 7t ₅ 220;

t _< 31.4 sec 27. 8 mi by canoe;

28

–

Trade-in Net Cost Payback Period ROI

Work van for a used small SUV $1500 ≈ _{21 mo or 1.7 yr 57.7%}

Compact car for a used hybrid $5000 ≈ _{96 mo or 8 yr 12.5%}

Work van for a new SUV $13,000 ≈ _{180 mo or 15 yr 6.7%}

Compact car for a new hybrid $13,500 ≈ _{259 mo or 21.6 yr 4.6%}

Older sedan for a new sedan $22,500 ≈ _{712 mo or 59.4 yr 1.7%}

Section 3.7

34. The trade-in of the work van for a small used SUV is the most justifiable, and the work van for a new hybrid and the compact car for a used hybrid may be

reasonably justifiable based on fuel savings and ROI. Note that other costs are not being considered.

35. w = 4 36. x = –0.7 37. y = 9 38. z = 1

2

39. t = vf vi a

−

; t = 15 sec 40. 50,000

41. $25,500 42. $96

43. 52%

44. The second discount was applied only to the

3.8 Mixtures

1. 14 gal 2. 0.65x lb 3. 7.2 oz 4. 33% 5. 80 L 6. $25.20 7. $5.31n

8. 16 L 9. 0.5x

10. 0.25(x + 80)

11. 18 gal; 7.6 gal; 42% salt 12. 50 gal; 4.92 gal; 9.84% 13. 42 gal; 33% acid

14. 15%

15. 4 lb of butter scotch and 16 lb of cinnamon balls 16. 15 gal of cream

17. 21 lb of Chinese and 14 lb of Indian

Section 3.8

19. 2 gal

20. 2.4 lb of Pistachio Pleasure; 9.6 lb of Pistachio Surprise 21. 2.5 L

22. 5 gal 23. 11%

24. 18 lb of hamburger and 12 lb of sausage

25. 3 cans of grapefruit and 4 cans of pineapple

29.

30. Car B retains 38% of its value in the first 6 yr, while Car A retains only 24% of its value.

31. 24 in. 32. 21 in.2

33. 8 mi/hr 34. 11

3

35. 12 games 36. 20.5 mi/hr

New 1 yr old 2 yr old 3 yr old 4 yr old 5 yr old 6 yr old

Value $27,370 $19,506 $16,453 $10,918 $8755 $7329 $6551 Car A

Percent Change 29% 16% 34% 20% 16% 11%

Value $29,045 $22,499 $18,829 $14,509 $14,031 $12,731 $11,112 Car B

Section 3.8

37. The school exceeded its goal by 5 students

38. 0.7 g/cm3; 6.2% 39. $0

Chapter 3 Review

1. m = dv

2. x = y b m

−

3. r = S ch c

−

4. c = b a −bd

5. A =

3

SR S

+

6. v₂ = a(t₂ – t₁) + v₁;

v₂ = 49 m/s

7. 275 words/page

9. 60 mi/hr 10. 27.7 m/sec 11. y = 125

3

≈ _41.6

12. x = 5

13. 10 g of hydrogen and 80 g of oxygen

14. 210 mi

15. 3 in.

16. 180 ft2

Chapter 3 Review

18. 56 cm

19. 134.4 cm2

20. 0.005, 1 200

21. 50%; 1 2 22. 0.2, 20%

23. 150

24. 475%

25. 4% increase; 936

26. subtract 50; 33.3% decrease

27. 175; 140

28. 87.5%

29. 120 people; 280 people

30. 7 PM

31. 47.7 mi/hr 32. 315 mi 33. 92.2%

34. 0.14 g/cm3; 5.2% 35. 3.6%

36. $9240; $9702 37. 38.5%

39. $15,000 40. $9200

41. $5000 at 4% and $10,000 at 6% 42. 1.5 hr

43. 5760 yd ≈ _{3.3 mi}

44. 3 hr

45. 30 lb of Columbian and 20 lb of Brazilian

46. 315 children and 735 adults 47. 6.6 L

Sequences—Fibonacci and Golden Ratio Sequences

1. 7, 12, 19, 31, 50 2. 9, 10, 19, 29, 48 3. –1, 2, 1, 3, 4 4. 5

2, 7 5,

12 7 ,

19 12,

31 19

5. 1, 2, 3

2, 5 3,

8 5

6. 13

8 , 21 13,

34 21,

55 34,

89 55