Elementary Algebra 2e

# Chapter 5

### Be Prepared

5.1

(a) yes (b) no

5.2

$m=3;m=3;$ $b=−12b=−12$

5.4

$−15+5x−15+5x$

5.5

$−2n−6−2n−6$

5.6

$y=4y=4$

5.7

$x=3y−1x=3y−1$

5.8

$−30+15a−30+15a$

5.9

$x=2x=2$

5.10

$1111$

5.11

Jon earned $22,00022,000$ and Ron earned $74,00074,000$.

5.12

$3535$ miles

5.13

$6, 287.056, 287.05$

5.14

$0.0820.082$

5.15

$5.855.85$

5.17

$a>−4a>−4$

5.18

no

### Try It

5.1

yes no

5.2

no yes

5.3

$(3,2)(3,2)$

5.4

$(2,3)(2,3)$

5.5

$(−2,−2)(−2,−2)$

5.6

$(1,6)(1,6)$

5.7

$(3,4)(3,4)$

5.8

$(5,−4)(5,−4)$

5.9

$(4,2)(4,2)$

5.10

$(−3,5)(−3,5)$

5.11

$(9,−1)(9,−1)$

5.12

$(4,−6)(4,−6)$

5.13

no solution

5.14

no solution

5.15

infinitely many solutions

5.16

infinitely many solutions

5.17

no solution, inconsistent, independent

5.18

no solution, inconsistent, independent

5.19

one solution, consistent, independent

5.20

one solution, consistent, independent

5.21

infinitely many solutions, consistent, dependent

5.22

infinitely many solutions, consistent, dependent

5.23

Manny needs 3 quarts juice concentrate and 9 quarts water.

5.24

Alisha needs 15 ounces of coffee and 3 ounces of milk.

5.25

$(6,1)(6,1)$

5.26

$(4,2)(4,2)$

5.27

$(2,4)(2,4)$

5.28

$(−1,−3)(−1,−3)$

5.29

$(1,−2)(1,−2)$

5.30

$(2,6)(2,6)$

5.31

$(−2,−3)(−2,−3)$

5.32

$(6,2)(6,2)$

5.33

$(6,2)(6,2)$

5.34

$(8,2)(8,2)$

5.35

$(2,32)(2,32)$

5.36

$(−12,−2)(−12,−2)$

5.37

infinitely many solutions

5.38

infinitely many solutions

5.39

no solution

5.40

no solution

5.41

The numbers are 3 and 7.

5.42

The numbers are 2 and −8.

5.43

The length is 12 and the width is 8.

5.44

The length is 23 and the width is 6.

5.45

The measure of the angles are 22 degrees and 68 degrees.

5.46

The measure of the angles are 36 degrees and 54 degrees.

5.47

There would need to be 160 policies sold to make the total pay the same.

5.48

Kenneth would need to sell 1,000 suits.

5.49

$(2,−1)(2,−1)$

5.50

$(−2,3)(−2,3)$

5.51

$(3,−1)(3,−1)$

5.52

$(−2,5)(−2,5)$

5.53

$(1,1)(1,1)$

5.54

$(−2,4)(−2,4)$

5.55

$(1,3)(1,3)$

5.56

$(4,−3)(4,−3)$

5.57

$(6,2)(6,2)$

5.58

$(1,−2)(1,−2)$

5.59

infinitely many solutions

5.60

infinitely many solutions

5.61

no solution

5.62

no solution

5.63

The numbers are 25 and 17.

5.64

The numbers are −25 and 10.

5.65

The bag of diapers costs $11 and the can of formula costs$13.

5.66

There are 105 calories in a banana and 5 calories in a strawberry.

5.67

Since both equations are in standard form, using elimination will be most convenient. Since one equation is already solved for $xx$, using substitution will be most convenient.

5.68

Since one equation is already solved for $yy$, using substitution will be most convenient; Since both equations are in standard form, using elimination will be most convenient.

5.69

${m+n=−23m=n−7{m+n=−23m=n−7$

5.70

${m+n=−18m=n+40{m+n=−18m=n+40$

5.71

${w+h=84,000h=2w−18,000{w+h=84,000h=2w−18,000$

5.72

${s=2n−5s+n=43{s=2n−5s+n=43$

5.73

Ali is 26 and Jameela is 14.

5.74

Jake is 9 and his dad is 33.

5.75

Mark burned 11 calories for each minute of yoga and 7 calories for each minute of jumping jacks.

5.76

Erin burned 11 calories for each minute on the rowing machine and 5 calories for each minute of weight lifting.

5.77

The angle measures are 55 degrees and 35 degrees.

5.78

The angle measures are 5 degrees and 85 degrees.

5.79

The angle measures are 42 degrees and 138 degrees.

5.80

The angle measures are 66 degrees and 114 degrees.

5.81

The length is 60 feet and the width is 35 feet.

5.82

The length is 60 feet and the width is 38 feet.

5.83

It will take Clark 4 hours to catch Mitchell.

5.84

It will take Sally $112112$ hours to catch up to Charlie.

5.85

The rate of the boat is 11 mph and the rate of the current is 1 mph.

5.86

The speed of the canoe is 7 mph and the speed of the current is 1 mph.

5.87

The speed of the jet is 236 mph and the speed of the wind is 29 mph.

5.88

The speed of the jet is 408 mph and the speed of the wind is 24 mph.

5.89

There were 206 adult tickets sold and 347 children tickets sold.

5.90

There were 521 adult tickets sold and 842 children tickets sold.

5.91

Matilda has 13 dimes and 29 quarters.

5.92

Juan has 36 nickels and 63 dimes.

5.93

Greta should use 3 pounds of peanuts and 2 pounds of cashews.

5.94

Sammy should purchase 10 pounds of beans and 10 pounds of ground beef.

5.95

LeBron needs 120 ml of the 25% solution and 30 ml of the 50% solution.

5.96

Anatole should mix 125 ml of the 10% solution and 125 ml of the 40% solution.

5.97

Leon should put $42,000 in the stock fund and$8000 in the savings account.

5.98

Julius invested $1,750 at 11% and$5,250 at 13%.

5.99

The principal amount for the bank loan was $4,000. The principal amount for the federal loan was$14,000.

5.100

The principal amount for was $41,200 at 4.5%. The principal amount was,$24,000 at 7.2%.

5.101

no yes

5.102

no no

5.109

no solution

5.110

no solution

5.111

$y≥3x+1y≥3x+1$

5.112

$x+4y≤4x+4y≤4$

5.113
1. ${30m+20p≤1602m+3p≤15{30m+20p≤1602m+3p≤15$

2. yes
3. no
5.114
1. ${a≥p+5a+2p≤400{a≥p+5a+2p≤400$

2. no
3. no
5.115
1. ${0.75d+2e≤25360d+110e≥1000{0.75d+2e≤25360d+110e≥1000$

2. yes
3. no
5.116
1. ${140p+125j≥10001.80p+1.25j≤12{140p+125j≥10001.80p+1.25j≤12$

2. yes
3. no

### Section 5.1 Exercises

1.

yes no

3.

yes no

5.

yes no

7.

no yes

9.

$(−2,3)(−2,3)$

11.

$(1,2)(1,2)$

13.

$(0,2)(0,2)$

15.

$(2,4)(2,4)$

17.

$(2,−1)(2,−1)$

19.

$(1,2)(1,2)$

21.

$(3,2)(3,2)$

23.

$(1,1)(1,1)$

25.

$(−1,−4)(−1,−4)$

27.

$(−2,−2)(−2,−2)$

29.

$(3,3)(3,3)$

31.

$(6,−2)(6,−2)$

33.

$(3,2)(3,2)$

35.

$(1,3)(1,3)$

37.

$(−3,1)(−3,1)$

39.

no solution

41.

no solution

43.

infinitely many solutions

45.

infinitely many solutions

47.

infinitely many solutions

49.

$(2,2)(2,2)$

51.

0 solutions

53.

0 solutions

55.

no solutions, inconsistent, independent

57.

consistent, 1 solution

59.

infinitely many solutions

61.

infinitely many solutions

63.

Molly needs 16 ounces of strawberry juice and 48 ounces of water.

65.

Enrique needs 8 ounces of nuts and 16 ounces of water.

67.

Leo should plant 50 tulips and 300 daffodils.

69.

Given that it is only known that the slopes of both linear equations are the same, there are either no solutions (the graphs of the equations are parallel) or infinitely many.

### Section 5.2 Exercises

71.

$(−2,0)(−2,0)$

73.

$(7,6)(7,6)$

75.

$(0,3)(0,3)$

77.

$(6,−3)(6,−3)$

79.

$(3,−1)(3,−1)$

81.

$(6,6)(6,6)$

83.

$(5,0)(5,0)$

85.

$(−2,7)(−2,7)$

87.

$(−5,2)(−5,2)$

89.

$(−1,7)(−1,7)$

91.

$(−3,5)(−3,5)$

93.

(10, 12)

95.

$(12,3)(12,3)$

97.

$(12,−34)(12,−34)$

99.

Infinitely many solutions

101.

Infinitely many solutions

103.

No solution

105.

No solution

107.

The numbers are 6 and 9.

109.

The numbers are −7 and −19.

111.

The length is 20 and the width is 10.

113.

The length is 34 and the width is 8.

115.

The measures are 16° and 74°.

117.

The measures are 45° and 45°.

119.

80 cable packages would need to be sold.

121.

Mitchell would need to sell 120 stoves.

123.

$t=2t=2$ hours $s=212s=212$ hours

125.

### Section 5.3 Exercises

127.

(6, 9)

129.

$(−2,1)(−2,1)$

131.

$(−7,−1)(−7,−1)$

133.

$(−2,−4)(−2,−4)$

135.

$(−1,3)(−1,3)$

137.

$(−1,2)(−1,2)$

139.

$(−5,9)(−5,9)$

141.

(6, 1)

143.

$(−2,10)(−2,10)$

145.

(2, 3)

147.

$(−7,6)(−7,6)$

149.

$(−9,3)(−9,3)$

151.

(9, 5)

153.

$(−3,2)(−3,2)$

155.

$(−2,3)(−2,3)$

157.

infinitely many solutions

159.

infinitely many solutions

161.

infinitely many solutions

163.

inconsistent, no solution

165.

inconsistent, no solution

167.

The numbers are 20 and 45.

169.

The numbers are 16 and −43.

171.

A shirt costs $16 and a sweater costs$33.

173.

There are 860 mg in a hot dog. There are 1,000 mg in a cup of cottage cheese.

175.

elimination substitution

177.

substitution elimination

179.

$r=4r=4$ $c=1c=1$

181.
1. (8, 2)

### Section 5.4 Exercises

183.

The numbers are 6 and 9.

185.

The numbers are −5 and −25.

187.

The numbers are 5 and 4.

189.

The numbers are 2 and 3.

191.

$10,000 193. She put$15,000 into a CD and $35,000 in bonds. 195. The amount of the first year’s loan was$30,000 and the amount of the second year’s loan was $12,000. 197. Bethany is 16 years old and Alyssa is 28 years old. 199. Noelle is 20 years old and her dad is 54 years old. 201. The small container holds 20 gallons and the large container holds 30 gallons. 203. There were 10 calories burned jogging and 10 calories burned cycling. 205. Notebooks are$4 and thumb drives are $20. 207. The measures are 60 degrees and 30 degrees. 209. The measures are 125 degrees and 55 degrees. 211. 94 degrees and 86 degrees 213. 72.5 degrees and 17.5 degrees 215. The measures are 44 degrees and 136 degrees. 217. The measures are 34 degrees and 56 degrees. 219. The width is 10 feet and the length is 25 feet. 221. The width is 15 feet and the length is 15 feet. 223. It took Sarah’s sister 12 hours. 225. It took Lucy’s friend 2 hours. 227. The canoe rate is 5 mph and the current rate is 1 mph. 229. The boat rate is 6.60 mph and the current rate is 2.50 mph. 231. The jet rate is 240 mph and the wind speed is 28 mph. 233. The jet rate is 415 mph and the wind speed is 19 mph. 235. $s=183,a=242s=183,a=242$ 237. Answers will vary. ### Section 5.5 Exercises 239. There 1120 adult tickets and 530 child tickets sold. 241. Josie bought 40 adult tickets and 32 children tickets. 243. There were 125 adult tickets and 128 children tickets sold. 245. Brandon has 12 quarters and 8 dimes. 247. Peter had 11 dimes and 48 quarters. 249. The cashier has fourteen$10 bills and sixteen $20 bills. 251. Marissa should use 60 pounds of the$1.20/lb candy and 30 pounds of the $1.80/lb candy. 253. Hannah needs 10 gallons of soda and 15 gallons of fruit drink. 255. Julia and her husband should buy 12 pounds of City Roast Columbian coffee and 8 pounds of French Roast Columbian coffee. 257. Jotham should mix 42 liters of the 30% solution and 28 liters of the 80% solution. 259. The scientist should mix 15 liters of the 25% solution and 50 liters of the 12% solution. 261. 160 liters of the 40% solution and 80 liters of the 70% solution will be used. 263. Hattie should invest$900 at 12% and $2,100 at 10%. 265. Sam invested$28,000 at 10% and $20,000 at 6%. 267. The federal loan is$62,500 and the bank loan is $3,300. 269.$12,000 should be invested at 5.25% and $13,000 should be invested at 4%. 271. 14 boys paid the full-year fee. 4 boys paid the partial-year fee, 273. Answers will vary. ### Section 5.6 Exercises 275. true false 277. false true 279. true false 281. true true 283. 285. 287. 289. 291. 293. 295. 297. 299. 301. 303. 305. No solution 307. No solution 309. 311. $x+4y<6x+4y<6$ 313. $−2x+6y>8−2x+6y>8$ 315. 1. ${p+l≥6015p+10l≥800{p+l≥6015p+10l≥800$ 2. No 3. Yes 317. 1. ${7p+3c≤500p≥2c+4{7p+3c≤500p≥2c+4$ 2. Yes 3. No 319. 1. ${90b+150g≥5000.35b+2.50g≤15{90b+150g≥5000.35b+2.50g≤15$ 2. No 3. Yes 321. 1. ${7c+11p≥35110c+22p≤200{7c+11p≥35110c+22p≤200$ 2. Yes 3. No 323. 1. ${3a+3c<752a+4c<62{3a+3c<752a+4c<62$ 2. No 3. Yes 325. Answers will vary. ### Review Exercises 327. no yes 329. $(3,−3)(3,−3)$ 331. $(5,4)(5,4)$ 333. coincident lines 335. infinitely many solutions, consistent system, dependent equations 337. no solutions, inconsistent system, independent equations 339. LaVelle needs 8 ounces of chocolate syrup and 40 ounces of coffee. 341. $(−1,2)(−1,2)$ 343. $(−2,−2)(−2,−2)$ 345. no solution 347. The numbers are 22 and 33. 349. The measures are 23 degrees and 67 degrees. 351. $(1,11)(1,11)$ 353. $(4,−1)(4,−1)$ 355. $(−2,5)(−2,5)$ 357. The numbers are $−37−37$ and $−53−53$. 359. elimination 361. ${x+y=−32x=2y−2{x+y=−32x=2y−2$ The numbers are –10 and –22 363. ${j+d=7200d=j+1600{j+d=7200d=j+1600$ Debbie earned$4400 and Jim earned $2800 365. Pam is 51 and Jan is 48. 367. The measures are 119 degrees and 61 degrees. 369. The pergola is 8 feet high and 12 feet wide. 371. It will take Lenore 3 hours. 373. The rate of the boat is 10.5 mph. The rate of the current is 1.5 mph. 375. Lynn bought 227 student tickets and 34 adult tickets. 377. Yumi should use 4 cups of candies and 8 cups of nuts. 379. Jack should put$3600 into savings and \$8400 into the CD.

381.

yes yes

383.
385.
387.

No solution

389.

${b+n≤4012b+18n≥500{b+n≤4012b+18n≥500$

yes
no

### Practice Test

391.

yes no

393.
395.

$(4,−7)(4,−7)$

397.

infinitely many solutions

399.

The numbers are 40 and –64

401.

The measures of the angles are 28 degrees and 62 degrees.

403.

It will take Kathy $1616$ of an hour (or 10 minutes).

405.

Liz bought 23 children’s tickets and 5 adult tickets.

407.

${C+0.5L≤50L≥3C{C+0.5L≤50L≥3C$

No
Yes

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