Chapter 2 Linear Equations and Inequalities in One Variable
109. Let x = number of miles driven.
80 0.25 400
x
110. Let x = the number of miles driven.
60 0.50 600
111. Let x = number of cement bags.
245 95 3000
245 95 245 3000 245
x
x
112. Let x = the number of cement bags.
265 65 2800
265 65 265 2800 265
x
x
113. – 116. Answers will vary.
117. makes sense
118. makes sense
122. false; Changes to make the statement true will vary.
A sample change is: The statement “x is at most 5”
125. Let x = number of miles driven.
Weekly cost for Basic Rental: $260.
Weekly cost for Continental: $80 + 0.25x
0.25 0.25
720
x
Basic Car Rental is a better deal if you drive more
than 720 miles in a week.
500 440 1.75xx
Solve this inequality.
500 1.75 440 1.75 1.75
xx xx
out more than 80 hours a year.
127. 1.45 7.23 1.442
1.45 7.23 1.45 1.442 1.45
7.23 2.892
x
x
x
Chapter 2 Review Exercises
128. 126.8 9.4 4.8 34.5
126.8 9.4 4.8 4.8 34.5 4.8
yy
yy y y
129. A = PB, A = 8, P = 40% = 0.4
A
PB
130. Let xthe width of the rectangle.
Let 5xthe length of the rectangle.
22
34 2( 5) 2
Plw
xx
131.
5163 8
516324
5163 3243
21624
xx
xx
xxxx
x
132.
414
24(3)14
xy
814,false
No, the values make it a false statement.
3
y
Chapter 2 Review Exercises
The solution is set is
22 .
3.
7369
736 696
39
zz
zzzz
z
Chapter 2 Linear Equations and Inequalities in One Variable
4.
4 3310
412310
xx
xx
5.
6391573
3823
382 232
xx xx
xx
xxxx
6.
10
8
8810
8
80
x
x
x
The solution is set is
80 .
8.
777
777
77
11
z
z
z
The solution is set is
11 .
10.
39
5
x
11.
5
30 2
225
30
y
y
25
x
The solution is set is
25 .
13.
1
10
10 10 1
x
x
499339
424
424
44
6
x
x
x
x
The solution is set is
6.
Chapter 2 Review Exercises
16.
5203
5203 33
2200
zz
zzzz
z
17.
53 5
53 5
435
xx
xxxx
x
18.
32 98
32 8 98 8
36 9
36 3 93
xx
xx xx
x
x
19. a. 2012 is 5 years after 2007.
0.9 15
0.9(5) 15 19.5
pn
p
According to the formula, 19.5% of Americans
were religiously unaffiliated in 2012.
20.
5976 18
215 18
215 18
xxx
xx
xxxx
21.
34512
312512
xx
xx
x
The solution is set is
12 .
22.
126 3 2
112 2 3 2
13
yy
yy
y
The solution is set is
13 .
23. 2831522
xx x
Chapter 2 Linear Equations and Inequalities in One Variable
24.
2432262
2832262
510 6
yy y
yy y
yy
25. 21
36
xx
To clear fractions, multiply both sides by the LCD,
which is 6.
2
661
36
xx
26. 11
210 52
xx
Multiply both sides by the LCD, which is 10.
11
10 10
210 52
xx
27. Multiply both sides by 100 to clear the decimals.
0.5 8.75 13.25
100(0.5 8.75) 100(13.25)
x
x
0.1( 3) 1.1 0.25
0.1 0.3 1.1 0.25
100(0.1 0.3) 100(1.1 0.25 )
10 30 110 25
10 140 25
xx
xx
xx
xx
xx
330
Since −3 = 30 is a false statement, the original
equation is inconsistent and has no solution or
.
30.
42 3 4 8 8
xx
Chapter 2 Review Exercises
31.
0.7 220
133 0.7 220
Ha
a
32. I = Pr for r
or
IPr
PP
II
rr
PP
33. 1 for
VBhh
34. 2 2 for Plw w
222 2
22
22
22
22
or
22
Pl lwl
Pl w
Pl w
Pl Pl
ww
36. for TDpm m
TDDpmD
0.08 120
9.6
A
A
8% of 120 is 9.6
38. ; 90, 45% 0.45APBA P
90 0.45
90 0.45
0.45 0.45
B
B
40. Increase = Percent · Original
First, find the increase: 12 – 6 = 6
66
66
66
1
P
P
P
The percent increase is 100%.
Chapter 2 Linear Equations and Inequalities in One Variable
43. Investment dollars lost last year were
0.10 $10,000 $1000. This means that $10,000 −
$1000 = $9000 remains. Investment dollars gained
44. a.
7
77
h
r
h
r
45.
91 0.26
APB
B
46. Let x = the unknown number.
6204
6204 44
2200
xx
xxxx
x
47. Let x Buffett’s net worth.
Let
14x
Gate’s net worth.
(14)148
xx
193
2193
292
46
xx
x
x
x
2 2 2 100 2
298
x
x
50. Let xnumber of years after 2001.
7284 328 12,204
328 4920
328 4920
328 328
15
x
x
x
x
Chapter 2 Review Exercises
52. Let xthe width of the field.
Let
3x
the length of the field.
22
400 2 3 2
Plw
xx
53. Let xthe original price of the table.
0.25 180
0.75 180
0.75 180
0.75 0.75
240
xx
x
x
x
The table’s price before the reduction was $240.
56. Find the area of a trapezoid with bases 22 yd and 5
yd and height 10 yd.
1()
2
Ahab
57. Notice that the height of the middle rectangle is
64 12 12 40
m.
3000 4608
7608
The area is 7608 m
2
.
58. Since the diameter is 20 m, the radius is
20 10 m.
2
2 2 (10) 20 63C
ππ π
6
h
The height of the sail is 6 ft.
60. Area of floor:
2
(12 ft )(15 ft ) 180 ftAbh
Chapter 2 Linear Equations and Inequalities in One Variable
61. First, find the area of a trapezoid with bases 80 ft
and 100 ft and height 60 ft.
62. The radius of the medium pizza is
114 inches 7 inches,
2
and the radius of each
small pizza is
18 inches 4 inches.
2
Medium pizza:
22
22
(7 in.)
49 in. 154 in.
Ar
ππ
π
Small pizza:
63. Find the volume of a rectangular solid with length 5
cm, width 3 cm, and height 4 cm.
534 60Alwh
The volume is 60 cm
3
.
64. Find the volume of a cylinder with radius 4 yd and
height 8 yd.
65. Find the volume of a sphere with radius 6 m.
3
4
Vr
π
66. Find the volume of each box.
3
(8m)(4m)(3m) 96mVlwh
The volume of the tank is approximately 85 ft
3
.
Divide by 5 to determine how many fish can be put
in the tank.
84.82 16.96
5
There is enough water in the tank for 16 fish. Round
down to 16, since 0.96 of a fish cannot be
purchased.
68. The sum of the measures of the angles of any
440180
4140
35
x
x
x
If x = 35, then 2x + 15 = 2(35) + 15 = 85 and x + 25
= 35 + 25 = 60. The angles measure 85 , 35 , and
60 .
supplement is
180 75 105
.
72. Let x = the measure of the angle.
Let 90 – x = the measure of its complement.
Chapter 2 Review Exercises
73. Let x = the measure of the angle.
Let 180 – x = the measure of its supplement.
180 4 45
xx
74.
1x
75.
24x
78.
253
25535
28
28
22
4
x
x
x
x
x
,4
80.
35 18
35 3183
x
x
81.
465
46555
60
6606
xx
xxxx
x
x
6102 262
4106
41010610
416
416
44
4
xxxx
x
x
x
x
x
4,
Chapter 2 Linear Equations and Inequalities in One Variable
84.
22 4 4 2 6
48486
xx
xx
85.
24315
xxx
86. Let x = the student’s score on the third test.
42 74 60
3
42 74
3360
3
x
x
87. Let xthe number of people you invite to the
picnic.
350 55 2000
x
Chapter 2 Test
The solution set is
9.
2
525
525
55
5
x
x
x
The solution set is
5.
18 6 18 26 18
68
68
x
x
x
Chapter 2 Test
4.
32 4 9 3 1yy
612933
yy
5.
315
4
43 4 15
34 3
20
x
x
x
The solution set is
20 .
6. 11
10 3 5 2
xx
Multiply both sides by the LCD, 30.
11
30 30
10 3 5 2
xx
7. 9.2 80.1 21.3 19.6xx
To clear the equation of decimals, multiply both
sides by 10.
8. 2.4 180; 324Nx N
2.4 180 324
2.4 180 180 324 180
2.4 144
2.4 144
2.4 2.4
60
x
x
x
x
x
The US population is expected to reach 324 million
60 years after 1960, in the year 2020.
9.
2
for Vrhh
π
2
22
Vrh
rr
π
ππ
11. ; 6% 0.06, 140APBP B
0.06 140
8.4
A
A
6% of 140 is 8.4.
Chapter 2 Linear Equations and Inequalities in One Variable
12. ; A=120, 80% 0.80APB P
13. ; 12, 240APBA B
12 240
12 240
240 240
0.05
P
P
P
12 is 5% of 240.
14. Let x = the unknown number.
15. Let xthe average number of vacation days for
Americans.
Let 29xthe average number of vacation days
for Italians.
(29)55
29 55
xx
xx
17. Let x = the width of the field.
450 6
66
75
75
2 150
x
x
x
x
The field is 75 yards wide and 150 yards long.
18. Let x = the book’s original price.
height 22 meters.
11
47 22 517
22
Abh
The area of the triangle is 517 m
2
.
20. Find the area of a trapezoid with height 15 in, lower
Chapter 2 Test
21. Notice that the height of the side rectangle is
639ft.
A
22. Find the volume of a rectangular solid with length 3
in, width 2 in, and height 3 in.
323 18Vlwh
The volume is 18 in
3
.
23. Find the volume of a cylinder with radius 5 cm and
height 7 cm.
24. The area of the floor is
2
(40ft)(50ft) 2000 ft .A
The area of each tile is
2
(2ft)(2 ft) 4ft .A
25. 56, 8Ab
1
2
A
bh
26. Let x = the measure of the second angle.
Let 3x = the measure of the first angle.
Let x − 30 = the measure of the third angle.
3 ( 30) 180
xxx
106
2 106
53
xx
x
x
The measure of the angle is 53 .
28.
2,
30.
2
3
223
x
x
69 6 336
927
927
99
x
x
x
Chapter 2 Linear Equations and Inequalities in One Variable
32.
422 6
42212
xx
xx
33. Let x = the student’s score on the fourth exam.
76 80 72 80
x
34. Let x = the width of the rectangle.
2(20) 2 56
40 2 56
x
x
Cumulative Review Exercises (Chapters 1-2)
1.
81216 8 4 84 4
2.
32 246 8 2
5. The rational numbers are
1
8.
6(4 1 5 ) 6(4 ) 6(1) 6(5 )
24 6 30
xy x y
xy
9.
0.9 80
An
62 0.9 80
18 0.9
18 0.9
n
n
n
76 14
76 14
77 14
77 7 147
77
77
xx
xx x x
x
x
x
x
Cumulative Review
12.
2
53
xx
Multiply both sides by the LCD, 15.
15 2 15
53
xx
13.
1 for
3
VAhA
1
3
1
33
3
3
3
33
or
VAh
VAh
VAh
VAh
hh
VV
AA
hh
15. Let x = the width of the parking lot.
Let
210x
the length of the parking lot.
22
400 2(2 10) 2
400 4 20 2
Plw
xx
xx
16. Let x = number of gallons of gasoline.
0.40 30,000
0.40 30,000
0.40 0.40
75,000
x
x
x
75,000 gallons of gasoline must be sold.
17.
1
,2
Chapter 2 Linear Equations and Inequalities in One Variable
19. 52(3 ) 2(2 5)1xx
562 4 101
21411
xx
xx
20. Let xvalue of medical supplies sold.
600 0.04 2500
x