Back to Lesson 4-4
Name
Name
4-3B Lesson Master
USES
Questions on SPUR Objectives
Hours
Week
Davena
Jess
0
$125
$175
$225
$275
$325
$375
$50
$125
$200
$275
$350
$425
3
4
5
7. Complete the table to determine when the pools will contain the
same amount of water.
Jess
1. Complete the table to tell who will get the scooter first.
2
5
10
15
20
25
30
D = 125 + 50w;
J = 50 + 75w
2. Write the expressions that describe Davena’s and Jess’s
savings in terms of weeks.
3 weeks
3. What is the break-even point?
Yes, Davena would have bought the scooter first after 1 week.
To rent a mid-size car in Chicago, Rent-With-Us charges $37.99 per day
plus 20¢ per mile. Best Bet charges $39.99 per day plus 18¢ per mile.
40
60
80
100
120
Best Bet
$41.99
$45.99
$49.99
$53.99
$57.99
$61.99
$43.59
$47.19
$50.79
$54.39
$57.99
$61.59
Rent-With-Us:
37.99 + 0.20m
Best Bet:
39.99 + 0.18m
6. Write the expressions that describe the two companies’ charges.
176
15,000
30,000
45,000
60,000
75,000
90,000
20 hr
35 hr
30 hr
8. After how many hours will Deep Waters be empty?
9. How many hours will it take to fill Baby Fins?
Objective L
In 10–13, a canoe rental company charges a $20 fee plus $15 per hour
beyond 2 hours. Their competitor charges a $25 set fee plus $10 per hour
beyond 2 hours.
10. Write equations for the first rental company, R1, and its
competitor, R2, for their prices in terms of h hours when h ≥ 2.
R1 = 20 + 15(h – 2);
R2 = 25 + 10(h – 2)
100
90
80
70
60
50
40
30
20
10
c
R1
R2
Fee ($)
20
Rent-With-Us
Baby Fins (gal)
120,000
100,000
80,000
60,000
40,000
20,000
11. Graph both lines, with R1 and R2 as cost c on the y-axis and
h on the x-axis. Label the graphs.
Rent-With-Us
5. Complete the table to determine which company charges less for
driving 60 miles in a day.
Deep Waters (gal)
REPRESENTATIONS
4. If the scooter had cost only $175, would the answer to Question 1
change? Explain.
Miles
page 2
The Big Splash! water park has four swimming pools. Deep Waters, the
140,000-gallon pool, is being drained at a rate of 4,000 gallons per hour.
Baby Fins, the 90,000-gallon pool, is being filled at a rate of 3,000 gallons
per hour.
Objective I
Davena and Jess are both saving up for a $400 scooter. Davena has $125
saved and is saving at a rate of $50 per week. Jess has only $50 but is
saving at a rate of $75 per week.
1
4-3B
See pages 245–249 for objectives.
h
1 2 3 4 5 6 7 8 9 10 11 12
Hours
12. Use the intersection of the lines to determine the time at
which the prices break even.
3 hr
13. Write an inequality to describe for which hours R1 is a better
value and similar inequality for R2.
1
R is the better value when 0 < h < 3,
and R2 is a better value when h > 3.
Algebra
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Name
177
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Name
4-4A Lesson Master
SKILLS
Questions on SPUR Objectives
See pages 245–249 for objectives.
SKILLS
Objective A
In 1–8, solve and check.
x = _12
n=1
h = –_25
d = –85
1. 24x = 16 - 8x
3. 8n + 5n - 12 = n
5. 3(4h + 2) = 2(h +1)
d
7. __4 + 4 = __d5 - __14
PROPERTIES
4-4B Lesson Master
r=2
4. 9(a + 3) = 30a
a = _97
2
6. __3 (w + 9) = __94 w + 1
8. 7 - __15 x = 3(x + 1)
1. 25x = 10 - 5x
x = _13
45
w = –__
2
5
_
x=4
3. 45m - 38 = 5m - 158
m = –3
2. 5k + 21 = 17k - 3
k=2
4. 6a = 60 + 36a
a = –2
Objective F
5. 15y + 5y - 6 = 17y
1
9. __4 (x - 5) = __31 x + 3
Multiply both sides by 12.
Use the Distributive Property.
3x - 15 = 4x + 36
Add –4x to each side.
−x - 15 = 36
Add 15 to each side.
−x = 51
x = −51 Multiply (or divide) each side by –1.
3(x - 5) = 12 __31 x + 3
y=2
)
Copyright © Wright Group/McGraw-Hill
10. To solve 4x + 0.02 = 1.5x + 9, an effective first step is to add
to both sides.
USES
See pages 245–249 for objectives.
Objective A
In 1–16, solve and check.
2. 6r + 9 = 13r - 5
In 9, a sentence is solved. Fill in what was done.
(
Questions on SPUR Objectives
Answers vary.
Sample: –1.5x
7. 7t = 13t - 5 + 4t
t = _12
1
9. __4 ( j - 8) = __21 j + 2
j = –16
11. 4(h + 1) = 2(5h + 6)
h = –_43
Objective H
11. Consumer A gets a cellular telephone contract that requires
monthly payments of $34.99. Consumer B’s contract requires
monthly payments of 39.99 but offers him a $75 rebate when
he signs up.
5x
13. 4 - __
=x-2
7
Consumer A
Consumer B
b. After two years, who will have paid more?
c. After how many months will A and B have paid the same amount? 15 mo
6.4 yr
12. Suppose the city of Atlanta, GA has a population of 471,000 people
x = _72
a. After one year, who will have paid more?
f
2
15. __3 f + 6 = __4 - 2
96
f = –__
5
6. −3(2b - 5) = 3b
b = _53
h
2
h
2
8. __3 + __3 = __2 + __5
h = _85
10. 5(3n + 10) = 40n
n=2
(
)
3
1
2
–1
__
12. __5 s + __3 - __
10 s = 5
10
s = __
3
14. 5(2z + 1) = 5(z - 5)
z = –6
c
16. 8 + __9c = 2 __3 - 1
(
)
c = 18
that increases by 11,000 people every year, and that Washington, DC
has a population of 560,000 that decreases by 3,000 people each year.
To the nearest tenth of a year, how long will it be until the two cities
have about the same number of residents?
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