Chapter 1
Section 1.1 Check the answers for exercises 4-10 in a similar
manner.
1.
4.
2 x + 10 = 40
−7 m + 20 = 48
2 x + 10 − 10 = 40 − 10
−7 m + 20 − 20 = 48 − 20
2 x = 30
−7 m = 28
2 x 30
= −7 m 28
2 2 =
x = 15 −7 −7
m = −4
Check:
? 5.
2 (15 ) + 10 − 10 = 40 − 10
2.5 x + 7.5 = 32.5
?
30 + 0 = 30 2.5 x + 7.5 − 7.5 = 32.5 − 7.5
30 = 30 2.5 x = 25
2. 2.5 x 25
=
3x + 14 = 35 2.5 2.5
x = 10
3x + 14 − 14 = 35 − 14
3x = 21 6.
3x 21 3.4 x − 8.2 = 15.6
=
3 3 3.4 x − 8.2 + 8.2 = 15.6 + 8.2
x=7 3.4 x = 23.8
Check: 3.4 x 23.8
?
=
3.4 3.4
3 ( 7 ) + 14 = 35
x=7
?
21 + 14 = 35 7.
35 = 35
20 = 5.2 x − 0.8
3. 20 + 0.8 = 5.2 x − 0.8 + 0.8
−4t + 8 = −32 20.8 = 5.2 x
−4t + 8 − 8 = −32 − 8 20.8 5.2 x
=
−4t = −40 5.2 5.2
−4t −40 4=x
=
−4 −4 x=4
t = 10 8.
Check:
?
45 = −3.6c + 189
−4 (10 ) + 8 = − 32 45 − 189 = −3.6c + 189 − 189
?
−144 = −3.6c
−40 + 8 = − 32
−144 −3.6c
−32 = −32 =
−3.6 −3.6
40 = c
c = 40
1
© 2019 Cengage Learning, Inc. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
,9. 12. E = −17 w + 600
0.05 ( x − 200 ) = 240 a.
0.05 x − 10 = 240 E = −17(0) + 600 = 600
0.05 x − 10 + 10 = 240 + 10
The total enrollment in math classes at the college
0.05 x = 250
was 600 at the beginning of the fall semester.
0.05 x 250
=
0.05 0.05 b.
x = 5000 Let E = 430
10. 430 = −17 w + 600
0.03 ( n − 500 ) = 108 430 − 600 = −17 w + 600 − 600
0.03n − 15 = 108 −170 = −17 w
0.03n − 15 + 15 = 108 + 15 −170 −17
= w
0.03n = 123 −17 −17
10 = w
0.03n 123
= The total enrollment will be 430 ten weeks after the
0.03 0.03
n = 4100 start of the fall semester.
11. C = 10h + 20 c.
a. E = −17 w + 600
C = 10 (1) + 20 E = −17(8) + 600
C = 30 E = 464
After 1 hour of training, a new employee can After 8 weeks, enrollment in math classes at the
produce 30 candies per hour. college will be 464.
b. 13. P = 7.89q + 33.73
C = 10 ( 4 ) + 20 a.
C = 40 + 20 = 60 P = 7.89 ( 8 ) + 33.73
After 4 hours of training, a new employee can P = 63.12 + 33.73
produce 60 candies per hour. P = 96.85
c. In March 2017, there were approximately 96.85
Let C = 150 million Amazon Prime members in the United
150 = 10h + 20 States.
150 − 20 = 10h + 20 − 20 b.
130 = 10h P = 7.89q + 33.73
130 10h
= P = 7.89 ( 20 ) + 33.73
10 10
P = 157.8 + 33.73
13 = h
P = 191.53
A new employee can produce 150 candies per hour
In March 2020, there will be approximately 191.53
after 13 hours of training.
million Amazon Prime members in the United
States. This may be too many to make sense.
2
© 2019 Cengage Learning, Inc. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
, c. b.
Let P = 133. P = 1.5t − 300
133 = 7.89q + 33.73 P = 1.5 ( 400 ) − 300
133 − 33.73 = 7.89q + 33.73 − 33.73 P = 600 − 300
99.27 = 7.89q P = 300
99.27 7.89q If you sell 400 printed T-shirts, you will make $300
=
7.89 7.89 profit.
12.58 ≈ q
c.
In about May 2018 (about 12.6 quarters after
Let P = 1000
March 2015) the number of Amazon Prime 1000 = 1.5t − 300
members will reach about 133 million. 1000 + 300 = 1.5t − 300 + 300
14. p = 2.399 + 0.03w 1300 = 1.5t
a. 1300 1.5t
=
1.5 1.5
p = 2.399 + 0.03 ( 5 ) 866.67 ≈ t
p = 2.399 + 0.15
To make $1000 profit, you must sell 867 printed T-
p = 2.549
shirts.
Five weeks after the start of summer, the gas price
16. P = 5.5b − 500.50
is $2.549 per gallon.
a.
b.
P = 5.5(75) − 500.50
Let p = 2.759
P = 412.50 − 500.50
2.759 = 2.399 + 0.03w
P = −$88.00
2.759 − 2.399 = 2.399 − 2.399 + 0.03w
There is a loss of $88 dollars for selling only 75
0.360 = 0.03w
0.360 0.03w books.
=
0.03 0.03 b.
12 = w P = 5.5(b) − 500.50
Twelve weeks after the start of summer, the gas P = 5.5(200) − 500.50
price is $2.759 per gallon. P = 1100 − 500.50
15. P = 1.5t − 300 P = $599.50
a. There is a $599.50 profit for selling 200 books.
c.
P = 1.5 (100 ) − 300
Let P = 3600
P = 150 − 300
P = 5.5b − 500.50
P = −150
3600 = 5.5b − 500.50
If you sell 100 printed T-shirts, you will lose $150.
3600 + 500.50 = 5.5b − 500.50 + 500.50
4100.5 = 5.5b
4100.5 5.5
= b
5.5 5.5
745.545 = b
To make $3600 in profit, you must sell 746 books.
3
© 2019 Cengage Learning, Inc. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Section 1.1 Check the answers for exercises 4-10 in a similar
manner.
1.
4.
2 x + 10 = 40
−7 m + 20 = 48
2 x + 10 − 10 = 40 − 10
−7 m + 20 − 20 = 48 − 20
2 x = 30
−7 m = 28
2 x 30
= −7 m 28
2 2 =
x = 15 −7 −7
m = −4
Check:
? 5.
2 (15 ) + 10 − 10 = 40 − 10
2.5 x + 7.5 = 32.5
?
30 + 0 = 30 2.5 x + 7.5 − 7.5 = 32.5 − 7.5
30 = 30 2.5 x = 25
2. 2.5 x 25
=
3x + 14 = 35 2.5 2.5
x = 10
3x + 14 − 14 = 35 − 14
3x = 21 6.
3x 21 3.4 x − 8.2 = 15.6
=
3 3 3.4 x − 8.2 + 8.2 = 15.6 + 8.2
x=7 3.4 x = 23.8
Check: 3.4 x 23.8
?
=
3.4 3.4
3 ( 7 ) + 14 = 35
x=7
?
21 + 14 = 35 7.
35 = 35
20 = 5.2 x − 0.8
3. 20 + 0.8 = 5.2 x − 0.8 + 0.8
−4t + 8 = −32 20.8 = 5.2 x
−4t + 8 − 8 = −32 − 8 20.8 5.2 x
=
−4t = −40 5.2 5.2
−4t −40 4=x
=
−4 −4 x=4
t = 10 8.
Check:
?
45 = −3.6c + 189
−4 (10 ) + 8 = − 32 45 − 189 = −3.6c + 189 − 189
?
−144 = −3.6c
−40 + 8 = − 32
−144 −3.6c
−32 = −32 =
−3.6 −3.6
40 = c
c = 40
1
© 2019 Cengage Learning, Inc. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
,9. 12. E = −17 w + 600
0.05 ( x − 200 ) = 240 a.
0.05 x − 10 = 240 E = −17(0) + 600 = 600
0.05 x − 10 + 10 = 240 + 10
The total enrollment in math classes at the college
0.05 x = 250
was 600 at the beginning of the fall semester.
0.05 x 250
=
0.05 0.05 b.
x = 5000 Let E = 430
10. 430 = −17 w + 600
0.03 ( n − 500 ) = 108 430 − 600 = −17 w + 600 − 600
0.03n − 15 = 108 −170 = −17 w
0.03n − 15 + 15 = 108 + 15 −170 −17
= w
0.03n = 123 −17 −17
10 = w
0.03n 123
= The total enrollment will be 430 ten weeks after the
0.03 0.03
n = 4100 start of the fall semester.
11. C = 10h + 20 c.
a. E = −17 w + 600
C = 10 (1) + 20 E = −17(8) + 600
C = 30 E = 464
After 1 hour of training, a new employee can After 8 weeks, enrollment in math classes at the
produce 30 candies per hour. college will be 464.
b. 13. P = 7.89q + 33.73
C = 10 ( 4 ) + 20 a.
C = 40 + 20 = 60 P = 7.89 ( 8 ) + 33.73
After 4 hours of training, a new employee can P = 63.12 + 33.73
produce 60 candies per hour. P = 96.85
c. In March 2017, there were approximately 96.85
Let C = 150 million Amazon Prime members in the United
150 = 10h + 20 States.
150 − 20 = 10h + 20 − 20 b.
130 = 10h P = 7.89q + 33.73
130 10h
= P = 7.89 ( 20 ) + 33.73
10 10
P = 157.8 + 33.73
13 = h
P = 191.53
A new employee can produce 150 candies per hour
In March 2020, there will be approximately 191.53
after 13 hours of training.
million Amazon Prime members in the United
States. This may be too many to make sense.
2
© 2019 Cengage Learning, Inc. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
, c. b.
Let P = 133. P = 1.5t − 300
133 = 7.89q + 33.73 P = 1.5 ( 400 ) − 300
133 − 33.73 = 7.89q + 33.73 − 33.73 P = 600 − 300
99.27 = 7.89q P = 300
99.27 7.89q If you sell 400 printed T-shirts, you will make $300
=
7.89 7.89 profit.
12.58 ≈ q
c.
In about May 2018 (about 12.6 quarters after
Let P = 1000
March 2015) the number of Amazon Prime 1000 = 1.5t − 300
members will reach about 133 million. 1000 + 300 = 1.5t − 300 + 300
14. p = 2.399 + 0.03w 1300 = 1.5t
a. 1300 1.5t
=
1.5 1.5
p = 2.399 + 0.03 ( 5 ) 866.67 ≈ t
p = 2.399 + 0.15
To make $1000 profit, you must sell 867 printed T-
p = 2.549
shirts.
Five weeks after the start of summer, the gas price
16. P = 5.5b − 500.50
is $2.549 per gallon.
a.
b.
P = 5.5(75) − 500.50
Let p = 2.759
P = 412.50 − 500.50
2.759 = 2.399 + 0.03w
P = −$88.00
2.759 − 2.399 = 2.399 − 2.399 + 0.03w
There is a loss of $88 dollars for selling only 75
0.360 = 0.03w
0.360 0.03w books.
=
0.03 0.03 b.
12 = w P = 5.5(b) − 500.50
Twelve weeks after the start of summer, the gas P = 5.5(200) − 500.50
price is $2.759 per gallon. P = 1100 − 500.50
15. P = 1.5t − 300 P = $599.50
a. There is a $599.50 profit for selling 200 books.
c.
P = 1.5 (100 ) − 300
Let P = 3600
P = 150 − 300
P = 5.5b − 500.50
P = −150
3600 = 5.5b − 500.50
If you sell 100 printed T-shirts, you will lose $150.
3600 + 500.50 = 5.5b − 500.50 + 500.50
4100.5 = 5.5b
4100.5 5.5
= b
5.5 5.5
745.545 = b
To make $3600 in profit, you must sell 746 books.
3
© 2019 Cengage Learning, Inc. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
