Chapter 2

$18x+30$

$3-2n$

$12$

$2x-6$

$0.045$

$60\%$

$16$

$w-3$

$63$

$0.35x+0.4$

$2c+3$

$0.042$

$15$ is greater than $x$.

$15<x$

$\frac{2}{5}x+4$

$-x+4$

$-7$

a. >; b. >; c. >; d. >

$12$

ⓐ no ⓑ yes

ⓐ yes ⓑ no

$m=2$

$a=0$

$u=2$

$x=4$

$p=\mathrm{-2}$

$q=\mathrm{-8}$

$y=-\frac{17}{5}$

$z=0$

identity; all real numbers

identity; all real numbers

conditional equation; $q=-\frac{9}{11}$

conditional equation; $k=\frac{201}{14}$

contradiction; no solution

contradiction; no solution

$x=\frac{1}{2}$

$x=\mathrm{-2}$

$x=12$

$u=\mathrm{-12}$

$n=2$

$m=\mathrm{-1}$

$r=1$

$s=\mathrm{-8}$

$n=9$

$d=16$

He bought two notebooks.

He did seven crosswords puzzles.

$3$

$6$

$\mathrm{-15},\mathrm{-8}$

$\mathrm{-29},11$

$\mathrm{-33},\mathrm{-32},\mathrm{-31}$

$\mathrm{-13},\mathrm{-12},\mathrm{-11}$

32, 34, 36

$\mathrm{-10},\mathrm{-8},\mathrm{-6}$

The average cost was $5,000.

The median price was $19,300.

ⓐ 36 ⓑ $26 ⓒ $125\%$

ⓐ 33 ⓑ $36 ⓒ $175\%$

25 grams

2,375 mg

50%

40%

$8.8\%$

50%

ⓐ $600 ⓑ $1,800

ⓐ $2,975 ⓑ $11,475

He will earn $2,500.

She earned $7,020.

The rate of simple interest was 6%.

The rate of simple interest was 5.5%.

He paid $17,590.

She deposited $9,600.

$b=\frac{2A}{h}$

$h=\frac{2A}{b}$

$C=\frac{5}{9}(F-32)$

$b=\frac{2A-Bh}{h}$

$t=\frac{A-P}{\text{P}r}$

$r=\frac{A-P}{\text{P}t}$

$y=\frac{9-4x}{7}$

$y=\frac{1-5x}{8}$

The window’s height is 12 meters.

The length of the base is 6 feet.

The measures of the angles are 20°, 70°, and 90°.

The measures of the angles are 30°, 60°, and 90°.

The length of the leg is 8.

The length of the leg is 12.

The length is 39 inches and the width is 16 inches.

The length is 17 yards and the width is 26 yards.

The lengths of the sides of the triangle are 5, 11 and 12 inches.

The lengths of the sides of the triangle are 4, 7 and 9 feet.

The length of the swimming pool is 70 feet and the width is 30 feet.

The length of the garden is 90 yards and the width is 60 yards.

The ladder reaches 12 feet.

He should attach the lights 8 feet from the base of the mast.

Jess has 41 nickels and 18 quarters.

Elane has 22 nickels and 59 dimes.

Eric bought thirty-two 49-cent stamps and twelve 35-cent stamps.

Kailee bought twenty-six 49-cent stamps and ten 20-cent stamps.

84 adult tickets, 31 student tickets

615 children’s tickets and 195 adult tickets

Orlando mixed five pounds of cereal squares and 25 pounds of nuts.

Becca mixed 21 gallons of fruit punch and seven gallons of soda.

The speed of the local train is 48 mph and the speed of the express train is 60 mph.

Jeromy drove at a speed of 80 mph and his mother drove 60 mph.

Christopher’s speed was 50 mph and his parents’ speed was 40 mph.

Ashley’s parents drove 55 mph and Ashley drove 62 mph.

Pierre and Monique will be 429 miles apart in 3 hours.

Thanh and Nhat will be 330 miles apart in 2.2 hours.

Suzy’s speed uphill is $1.8$ mph and downhill is three mph.

The boat’s speed upstream is eight mph and downstream is12 mph.

Hamilton drove 40 mph in the city and 70 mph in the desert.

Phuong rode uphill at a speed of 12 mph and on the flat street at 20 mph.

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Angie can buy 7 packs of juice.

Daniel can have 11 people at the party.

Sergio and Lizeth can travel no more than 500 miles.

Rameen can use no more than 76 therms.

Caleb must work at least 96 hours.

Elliot must work at least 85 jobs.

Brenda must babysit at least 27 hours.

Josue must shovel at least 20 driveways.

The homeowner can use 5–20 hcf and still fall within the “conservation usage” billing range.

The homeowner can use 16–40 hcf and still fall within the “normal usage” billing range.

ⓐ $\text{±}2$ ⓑ no solution ⓒ 0

ⓐ $\text{±}11$ ⓑ no solution ⓒ 0

$x=4,x=-\frac{2}{3}$

$x=\mathrm{-1},x=\frac{5}{2}$

$x=8,x=0$

$x=8,x=2$

No solution

No solution

$x=-\frac{2}{5},$ $x=\frac{5}{2}$

$x=3,$ $x=\frac{1}{9}$

The diameter of the rod can be between 79.991 and 80.009 mm.

The diameter of the rod can be between 74.95 and 75.05 mm.

ⓐ yes ⓑ no

ⓐ no ⓑ yes

$y=5$

$w=\mathrm{-18}$

$q=3$

$x=14$

$c=4$

$c=\frac{5}{2}$

$n=2$

$y=\mathrm{-5}$

$s=10$

$p=\mathrm{-4}$

$c=\mathrm{-4}$

$h=\frac{3}{4}$

$m=6$

identity; all real numbers

conditional equation;$j=\frac{2}{5}$

conditional equation; $m=\frac{16}{5}$

contradiction; no solution

contradiction; no solution

identity; all real numbers

$x=\mathrm{-1}$

$y=\mathrm{-1}$

$a=\frac{3}{4}$

$x=4$

$w=\frac{9}{4}$

$b=12$

$p=\mathrm{-41}$

$x=-\frac{5}{2}$

$n=\mathrm{-3}$

$x=\mathrm{-2}$

$u=3$

$x=18$

$x=20$

$n=9$

$d=8$

$L=19.75$ feet

Answers will vary.

Answers will vary.

Answers will vary.

Answers will vary.

six boys

58 hardback books

15

5

12

$\mathrm{-5}$

18, 24

8, 12

32, 46

4, 10

38, 39

25, 26, 27

$\mathrm{-11},\mathrm{-12},\mathrm{-13}$

84, 86, 88

$\mathrm{-69},\mathrm{-71},\mathrm{-73}$

$750

$13,500

ⓐ 54 ⓑ 108 ⓐ 30%

ⓐ $162.5$ ⓑ $35 ⓐ 150%

$\text{\$}11.88$

24.2 g

2407 mg

45%

25%

12%

200%

$\mathrm{-2.5}\%$

$\mathrm{-11}\%$

ⓐ $\text{\$}26.97$ ⓑ $\text{\$}17.98$

ⓐ $576 ⓑ 30%

ⓐ $\text{\$}7.20$ ⓑ $\text{\$}23.20$

ⓐ $\text{\$}0.20$ ⓑ $\text{\$}0.80$

$116

$4836

3%

$3.75\%$

$35,000

$3345

$21.2\%$

Answers will vary.

Answers will vary.

$d=\frac{C}{\pi }$

$L=\frac{V}{WH}$

$b=\frac{2A}{h}$

$d_1=\frac{2A}{d_2}$

$b_1=\frac{2A}{h}-b_2$

$a=\frac{2h-108t}{t^2}$

$a=180-b-c$

$p=\frac{2A-2B}{l}$

$L=\frac{P-2W}{2}$

$y=15-8x$

$y=\mathrm{-6}+4x$

$y=4+x$

$y=\frac{7-4x}{3}$

$y=\frac{12-2x}{3}$

$y=\frac{18-3x}{\mathrm{-2}}$

1 foot

23 inches

$45\text{°},45\text{°},90\text{°}$

$30\text{°},60\text{°},90\text{°}$

15

25

8

12

$10.2$

$9.8$

18 meters, 11 meters

$13.5$ m, $12.8$ m

25 ft, 50 ft

7 m, 11 m

12 ft, 13 ft, 14 ft

3 ft, 6 ft, 8 ft

120 yd, 160 yd

40 ft, 85 ft

5 feet

14.1 feet

$104\text{°}\text{F}$

240 ft

Answers will vary.

ⓐ Answers will vary. ⓑ The areas are the same. The $2\times 8$ rectangle has a larger perimeter than the $4\times 4$ square.
ⓒ Answers will vary.

nine nickels, 16 dimes

ten $10 bills, five $5 bills

63 dimes, 20 quarters

16 nickels, 12 dimes, seven quarters

330 day passes, 367 tournament passes

40 postcards, 100 stamps

15 $10 shares, five $12 shares

34 general, 61 youth

114 general, 246 student

Four pounds of macadamia nuts, eight pounds almonds

$3.6$ lbs Bermuda seed, $5.4$ lbs Fescue seed

$33,000 in Fund A, $22,000 in Fund B

$5.9\%$

Kathy 5 mph, Cheryl 3 mph

commercial 550 mph, private plane 340 mph

Violet 65 mph, Charlie 55 mph

Ethan 22 mph, Leo 16 mph

DaMarcus 16 mph, Fabian 22 mph

four hours

4.5 hours

uphill $1.6$ mph, downhill $4.8$ mph

light traffic 54 mph, heavy traffic 30 mph

freeway 67 mph, mountain road 22.3 mph

running eight mph, walking three mph

ⓐ 15 minutes ⓑ 20 minutes ⓒ one hour (d) 1:25

Answers will vary.

Answers will vary.

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A maximum of 14 people can safely ride in the elevator.

five drinks

86 cars

$16,875

$110,000

260 messages

35 people

32 jobs

62 necklaces

seven lawns

20 hours

20 people

42 guests

Answers will vary.

Answers will vary.

$5\le n\le 24$

$6\le w\le 12$

ⓐ answers vary ⓑ answers vary

Answers will vary.

ⓐ $x=4,x=\mathrm{-4}$ ⓑ no solution ⓒ $z=0$

ⓐ $x=3,x=\mathrm{-3}$ ⓑ no solution ⓒ $z=0$

$x=1,x=-\frac{1}{2}$

$x=\mathrm{-1},x=-\frac{5}{2}$

$x=7,x=1$

$x=1,x=\mathrm{-5}$

$x=7,x=1$

no solution

no solution

$x=\mathrm{-1},x=-\frac{2}{3}$

$x=\mathrm{-3},x=3$

$x=2,x=\frac{1}{4}$

$x=3,x=2$

$x=3,x=-\frac{11}{3}$

$x=\frac{3}{2},x=-\frac{1}{2}$

The minimum to maximum expected production is 207,500 to 2,225,000 bottles

The acceptable weight is 22.5 to 25.5 ounces.

Answers will vary.

no

$s=\mathrm{-22}$

$m=\mathrm{-14}$

$q=18$

$x=\mathrm{-1}$

$k=\frac{3}{4}$

contradiction; no solution

$n=2$

$k=23$

$x=5$

There are 116 people.

38

$\mathrm{-3},\mathrm{-10}$

76, 78, 80

$922

160

$\text{\$}3.89$

35%

32%

ⓐ $105 ⓑ $52.5\text{\%}$

$428.22

$1,900

$d_2=\frac{2A}{d_1}$

$y=\frac{4x}{3}-4$

$22.5\text{°},67.5\text{°},90\text{°}$

26

6 feet

$24.5$ cm, $12.5$ cm

9 ft, 14 ft, 12 ft

nine pennies, six dimes, 12 quarters

57 students, 68 general admission

$2.2$ lbs of raisins, $7.8$ lbs of nuts

$9.7\text{\%}$

Louellen 65 mph, Tracy 66 mph

upstream 3 mph, downstream 5 mph

heavy traffic 32 mph, light traffic 68 mph

$33 per day

at least $300,000

at least 112 jobs

$6\le w\le 12$

no solution

$x=2,x=\frac{2}{3}$

$x=9,x=\mathrm{-3}$

$x=2,x=\frac{1}{4}$

The minimum to maximum expected usage is 210,000 to 220,000 bottles

$x=\mathrm{-5}$

$a=41$

contradiction; no solution

$x=6$

$x=\mathrm{-2},x=-\frac{1}{3}$

$10.8$

$\mathrm{-57},\mathrm{-55}$

12 dimes, seven quarters

$30\text{°},60\text{°},90\text{°}$

$2.5$ hours

At most $55.56 per costume.