Elementary Algebra

# Chapter 3

Elementary AlgebraChapter 3

## Try It

3.1

$180 3.2 40 3.3 2 3.4 7 3.5 25 3.6 4 3.7 3 3.8 6 3.9 9, 15 3.10 27, 31 3.11 $−15 , −8 −15 , −8$ 3.12 $−29 , 11 −29 , 11$ 3.13 $−4 , 0 −4 , 0$ 3.14 $−3 , −2 −3 , −2$ 3.15 47, 48 3.16 $−16 , −15 −16 , −15$ 3.17 $−33 , −32 , −31 −33 , −32 , −31$ 3.18 $−13 , −12 , −11 −13 , −12 , −11$ 3.19 32, 34, 36 3.20 $−10 , −8 , −6 −10 , −8 , −6$ 3.21$5,000

3.22

$19,300 3.23 36 3.24 33 3.25$26

3.26

$36 3.27 125% 3.28 175% 3.29$14.67

3.30

$2.16 3.31 25 grams 3.32 2,375 mg 3.33 26% 3.34 40% 3.35 8.8% 3.36 50% 3.37 6.3% 3.38 10% 3.39$142.50

3.40

$7,020 3.41 6% 3.42 4% 3.43$11,450

3.44

$9,600 3.45$11.60 $17.40 3.46$256.75 $138.25 3.47$184.80 33%

3.48

$60 15% 3.49$600 $1,800 3.50$2,975 $11,475 3.51 9 nickels, 16 dimes 3.52 17 nickels, 5 quarters 3.53 42 nickels, 21 dimes 3.54 51 dimes, 17 quarters 3.55 41 nickels, 18 quarters 3.56 22 nickels, 59 dimes 3.57 330 day passes, 367 tournament passes 3.58 112 adult tickets, 199 senior/child tickets 3.59 84 adult tickets, 31 student tickets 3.60 26 full-fare, 14 reduced fare 3.61 32 at$0.41, 12 at $0.02 3.62 26 at$0.41, 10 at $0.20 3.63 5 pounds cereal squares, 25 pounds nuts 3.64 21 gallons of fruit punch, 7 gallons of soda 3.65$4,200 at 4%, $9,800 at 7% 3.66$2,500 at 3.2%, $5,500 at 8% 3.67 21 degrees 3.68 56 degrees 3.69 8 feet 3.70 6 feet 3.71 14 inches 3.72 6 feet 3.73 $34 ° 34 °$ 3.74 $45 ° 45 °$ 3.75 $20 ° , 70 ° , 90 ° 20 ° , 70 ° , 90 °$ 3.76 $30 ° , 60 ° , 90 ° 30 ° , 60 ° , 90 °$ 3.77 $c = 10 c = 10$ 3.78 $c = 13 c = 13$ 3.79 8 3.80 12 3.81 12 feet 3.82 8 feet 3.83 340 yards 3.84 220 feet 3.85 26 feet 3.86 29 meters 3.87 15 3.88 9 3.89 18 meters, 11 meters 3.90 19 feet, 11 feet 3.91 24, 8 3.92 5, 4 3.93 70 feet, 30 feet 3.94 90 yards, 60 yards 3.95 Wayne 21 mph, Dennis 28 mph 3.96 Jeromy 80 mph, mother 60 mph 3.97 Carina 50 mph, brother 65 mph 3.98 parents 55 mph, Ashley 62 mph 3.99 3 hours 3.100 2.2 hours 3.101 uphill 1.8 mph, downhill three mph 3.102 upstream 8 mph, downstream 12 mph 3.103 biking 16 mph, running 10 mph 3.104 uphill 12 mph, flat street 20 mph 3.105 There can be no more than 20 boxes. 3.106 A maximum of 14 people can safely ride in the elevator. 3.107 seven packs 3.108 11 people 3.109 at least$4,000,000

3.110

at least $1,200,000 3.111 no more than 106 text messages 3.112 no more than 76 therms 3.113 at least 96 hours 3.114 at least 1,380 invitations 3.115 at least 23 hours 3.116 at least 20 driveways ## Section 3.1 Exercises 1. Answers will vary 3. 30 5. 125 7. 6 9. 58 11.$750

13.

$13,500 15. 4 17. 15 19. 5 21. 12 23. $−5 −5$ 25. 18, 24 27. 8, 12 29. $−18 , −27 −18 , −27$ 31. $−111 , −205 −111 , −205$ 33. 32, 46 35. 23, 28 37. $−2 , −3 −2 , −3$ 39. 4, 10 41. 38, 39 43. $−11 , −12 −11 , −12$ 45. 25, 26, 27 47. $−11 , −12 , −13 −11 , −12 , −13$ 49. 84, 86, 88 51. 55, 57, 59 53. $−10 , −12 , −14 −10 , −12 , −14$ 55. $−69 , −71 , −73 −69 , −71 , −73$ 57.$45

59.

$1.25 61.$1080

63.

65.

Consecutive odd integers are odd numbers that immediately follow each other. An example of three consecutive odd integers between 50 and 60 would be 51, 53, and 55.

## Section 3.2 Exercises

67.

54

69.

26.88

71.

162.5

73.

18,000

75.

112

77.

108

79.

$35 81.$940

83.

30%

85.

36%

87.

150%

89.

175%

91.

$11.88 93.$259.80

95.

24.2 g

97.

2407 mg

99.

175 lb.

101.

$120 103. 18% 105. 45% 107. 25% 109. 12% 111. 200% 113. 72.7% 115. 2.5% 117. 11% 119. 5.5% 121.$116

123.

$4,836 125. 3% 127. 3.75% 129.$35,000

131.

$3,345 133.$139

135.

$125 137.$26.97 $17.98 139.$128.37 $260.63 141.$332.48 $617.47 143.$576 30%

145.

$53.25 15% 147.$370 43.5%

149.

$7.20$23.20

151.

$0.20$0.80

153.

$258.75$373.75

155.

21.2%

157.

The number should be greater than 44. Since 80% equals 0.8 in decimal form, 0.8 is less than one, and we must multiply the number by 0.8 to get 44, the number must be greater than 44.

159.

He meant that he should have packed half the shorts and twice the shirts.

## Section 3.3 Exercises

161.

8 nickels, 22 dimes

163.

15 dimes, 8 quarters

165.

10 at $1, 7 at$5

167.

18 quarters, 36 nickels

169.

30 pennies, 90 dimes

171.

10 at $10, 5 at$5

173.

12 dimes and 27 nickels

175.

63 dimes, 20 quarters

177.

16 nickels, 12 dimes, 7 quarters

179.

30 child tickets, 50 adult tickets

181.

110 child tickets, 50 adult tickets

183.

34 general, 61 youth

185.

114 general, 246 student

187.

40 postcards, 100 stamps

189.

30 at $0.41, 10 at$0.02

191.

15 $10 shares, 5$12 shares

193.

5 liters champagne, 10 liters orange juice

195.

7.5 lbs Maui beans, 17.5 Kona beans

197.

800 at $1.50, 200 at$9.00

199.

$8000 at 4%,$17,000 at 9%

201.

$10,000 in CD,$30,000 in mutual fund

203.

9.1%

205.

207.

209.

## Section 3.4 Exercises

211.

56 degrees

213.

44 degrees

215.

11 feet

217.

8 feet

219.

0.75 sq. ft.

221.

23 inches

223.

57

225.

67.5

227.

13 ft., 12 ft., 14 ft.

229.

3 ft., 6 ft., 8 ft.

231.

$45 ° , 45 ° , 90 ° 45 ° , 45 ° , 90 °$

233.

$30 ° , 60 ° , 90 ° 30 ° , 60 ° , 90 °$

235.

15

237.

25

239.

8

241.

12

243.

10.2

245.

9.8

247.

5 feet

249.

14.1 feet

251.

260 feet

253.

58 feet

255.

23 meters

257.

26 inches

259.

24

261.

4.9

263.

16 in., 7 in.

265.

17 m, 12 m

267.

13.5 m length, 12.8 m width

269.

50 ft., 25 ft.

271.

7 m width, 11 m length

273.

160 yd., 120 yd.

275.

85 ft., 40 ft.

277.

24 feet

279.

281.

The areas are the same.
The 2x8 rectangle has a larger perimeter than the 4x4 square.

## Section 3.5 Exercises

283.

Mason 75 mph, train 60 mph

285.

express bus 75mph, local 50 mph

287.

Saul 82 mph, Erwin 74 mph

289.

Helen 60 mph, Anne 56 mph

291.

Aletheia 2.4 mph, Elvira 3 mph

293.

3 hours

295.

3.5 hours

297.

walking 3 mph, jogging 4.5 mph

299.

upstream 6 mph, downstream 9 mph

301.

skateboarding 8 mph, walking 3.2 mph

303.

heavy traffic 30 mph, light traffic 70 mph

305.

36 mph 25 mph 3.05 hours 29.5 mph

307.

## Section 3.6 Exercises

309.

15 children

311.

12 people

313.

five drinks

315.

31 aprons

317.

$15,000 319.$400,000

321.

16 ccf

323.

nine movies

325.

48 cut & styles

327.

44 meals

329.

49 cars

331.

9 cars

333.

91 students

335.

169 guests

337.

## Review Exercises

339.

341.

116

343.

38

345.

$−18 , −9 −18 , −9$

347.

$−3 , −10 −3 , −10$

349.

$−48 , −47 , −46 −48 , −47 , −46$

351.

15, 17, 19

353.

167.5

355.

160

357.

120%

359.

$3.89 361.$875

363.

2.5%

365.

$428.22 367.$1,900

369.

$63 371.$55.20 $82.80 373.$70 15.6%

375.

$175$225

377.

16 dimes, 11 quarters

379.

six $5 bills, 11$10 bills

381.

383.

385.

three $0.26 stamps, eight$0.41 stamps

387.

2.2 lb. of raisins, 7.8 lb. of nuts

389.

$12,500 at 4.5%,$2,500 at 1.8%

391.

$73 ° 73 °$

393.

600 square inches

395.

$30 ° , 60 ° , 90 ° 30 ° , 60 ° , 90 °$

397.

$22.5 ° , 67.5 ° , 90 ° 22.5 ° , 67.5 ° , 90 °$

399.

26

401.

8

403.

8.1

405.

$6 ′ 6 ′$

407.

110 ft. 684 sq. ft.

409.

62 m

411.

24.5 cm, 12.5 cm

413.

Gabe 70 mph, Elsa 77 mph

415.

2.5 hours

417.

flat road 11 mph, uphill 8 mph

419.

$33 per day 421. at least$300,000

423.

at least 112 jobs

## Practice Test

425.

15

427.

$−49 , −47 −49 , −47$

429.

8%

431.

$208.50 30% 433. 140 adult, 85 children 435. $41.5 ° , 55.5 ° , 83 ° 41.5 ° , 55.5 ° , 83 °$ 437. 10 439. 127.3 ft. 441. 2.5 hours 443. at most$44.44 per costume

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