Basic Mathematics for College Students

8.5 Using Equations to Solve Application Problems 677

EXAMPLE (^2) Small Businesses Last
year, a stylist lost 17 customers who moved away.
If she now has 73 customers, how many did she
have originally?
Analyze

• She lost 17 customers. Given


• She now has 73 customers. Given


• How many customers did she originally have? Find

Form
We can let cthe original number of customers. To form an equation involving c,
we look for a key word or phrase in the problem.

Key phrase:moved away Translation:subtraction

Now we translate the words of the problem into an equation.

This is called the verbal model.

c  17  73

Solve

We need to isolate con the left side.

To isolate c, add 17 to both sides to undo the

subtraction of 17.

Do the addition.

State
She originally had 90 customers.

Check
If the hair stylist originally had 90 customers, and we decrease that number by the
17 that moved away, we should obtain the number of customers she has now.

This is the number of customers the hair stylist now has.

The result, 90, checks.

9

8

0

10

 17

73

c 90

c 17  17  73  17

c 17  73

the number of

is customers she has now.

minus^17

The original number

of customers

Self Check 2

GASOLINE STORAGEA tank

currently contains 1,325 gallons

of gasoline. If 450 gallons were

pumped from the tank earlier,

how many gallons did it originally

contain?

Now TryProblem 20

EXAMPLE (^3) Traffic Fines For speeding
in a construction zone, a motorist had to pay a fine of
$592. The violation occurred on a highway posted
with signs like the one shown on the right.What would
the fine have been if such signs were not posted?
Analyze

• For speeding, the motorist was fined $592. Given


• The fine was double what it would normally have been. Given


• What would the fine have been, had the sign not been posted? Find

Form
We can let fthe amount that the fine would normally have been. To form an
equation, we look for a key word or phrase in the problem or analysis.

Key word:double Translation:multiply by 2

TRAFFIC FINES

DOUBLED IN

CONSTRUCTION ZONE

Self Check 3

SPEED READINGA speed reading

course claims it can teach a

person to read four times faster.

After taking the course, a student

can now read 700 words per

minute. If the company’s claims

are true, what was the student’s

reading rate before taking the

course?

Now TryProblem 21

7

1

3

 17

90

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