98 CHAPTER 2 Linear Equations, Inequalities, and Applications
Using a Linear Inequality to Solve a Rental ProblemA rental company charges $15 to rent a chain saw, plus $2 per hr. Tom Ruhberg can
spend no more than $35 to clear some logs from his yard. What is the maximum
amount of time he can use the rented saw?
Step 1 Readthe problem again.
Step 2 Assign a variable.Let x the number of hours he can rent the saw.
Step 3 Write an inequality.He must pay $15, plus $2x, to rent the saw for xhours,
and this amount must be no more than$35.
Cost of is no
renting more than 35 dollars.35
Step 4 Solve. Subtract 15.
Divide by 2.Step 5 State the answer.He can use the saw for a maximum of 10 hr. (Of course,
he may use it for less time, as indicated by the inequality )
Step 6 Check.If Tom uses the saw for 10 hr, he will spend
dollars, the maximum amount.
15 + 21102 = 35
x...10.
x... 10
2 x... 20
15 + 2 x ...
=
EXAMPLE 8
NOW TRYIn Example 8,we use the six problem-solving steps from Section 2.3,changing
Step 3 from
“Write an equation” to “Write an inequality.”
NOW TRY
EXERCISE 8
A local health club charges a
$40 one-time enrollment fee,
plus $35 per month for a
membership. Sara can spend
no more than $355 on this ex-
ercise expense. What is the
maximumnumber of months
that Sara can belong to this
health club?
NOW TRY ANSWERS
- 9 months
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NOW TRY
EXERCISE 9
Joel has scores of 82, 97, and
93 on his first three exams.
What score must he earn on
the fourth exam to keep an
average of at least 90?
- at least 88
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Finding an Average Test ScoreMartha has scores of 88, 86, and 90 on her first three algebra tests. An average score
of at least 90 will earn an A in the class. What possible scores on her fourth test will
earn her an A average?
Let the score on the fourth test. Her average score must be at least 90. To
find the average of four numbers, add them and then divide by 4.
is at
Average least 90.90
Add the scores.Multiply by 4.
Subtract 264.