Basic Mathematics for College Students

678 Chapter 8 An Introduction to Algebra

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

2  f  592

Solve

We need to isolate fon the left side.

Do the division.

State

The fine would normally have been $296.

Check

If the normal fine was $296, and we double it, we should get the new fine.

This is the new fine.

The result, $296, checks.



2

1

9

1

6

 2

592

f 296

To isolate f, divide both sides by 2 to undo the

(^) multiplication by 2.
2 f
2



592

2

2 f 592

the new

is fine.

the normal

times speeding fine

Tw o

EXAMPLE (^4) Entertainment Costs A five-piece band worked on
New Year’s Eve. If each player earned $120, what fee did the band charge?
Analyze

• There were 5 players in the band. Given


• Each player made $120. Given


• What fee did the band charge? Find
  Form
  We can let fthe band’s fee. To form an equation, we look for a key word or
  phrase. In this case, we find it in the analysis of the problem. If each player earned
  the same amount ($120), the band’s fee must have been divided into 5 equal parts.
  Key phrase:divided into 5 equal parts Translation:division
  Now we translate the words of the problem into an equation.

f  5  120

Solve

We need to isolate fon the left side.

Do the multiplication.

State

The band’s fee was $600.

f 600

To isolate f, multiply both sides by 5 to undo the

5  division by 5.

f

5

 5  120

f

5

 120

each person’s

share.

is

the number of

players in the band

divided

by

The

band’s fee

Self Check 4

CLASSICAL MUSICA woodwind

quartet was hired to play at an art

exhibit. If each member made $85

for the performance, what fee did

the quartet charge?

Now TryProblem 22

296

(^2)  592
 4
19
 18
12
 12
0
1
1
20
 5
600