Basic Mathematics for College Students

8.5 Using Equations to Solve Application Problems 681

EXAMPLE (^7) Civil Service A candidate for a position with the FBI
scored 12 points higher on the written part of the civil service exam than she did on
her interview. If her combined score was 92, what were her scores on the interview
and on the written part of the exam?
Analyze

• She scored 12 points higher on the written part than on the
  interview. Given


• Her combined score was 92. Given


• What were her scores on the interview and on the written part? Find

Form
Since we are told that her score on the written part was related to her score on the
interview, we let xher score on the interview.
There is a second unknown quantity—her score on the written part of the
exam. We look for a key phrase to help us decide how to represent that score using
an algebraic expression.

Key phrase: 12 points higheron the Translation: add 12 points to the

written part than on interview score

the interview

So x 12 her score on the written part of the test. Now we translate the words
of the problem into an equation.

x  x 12  92

Solve

We need to isolatexon the left side.

On the left side, combine like terms: xx 2 x.

To isolate the variable term, 2x, subtract 12 from both

sides to undo the addition of 12.

Do the subtraction.

Do the division. This is her score on the interview.

To find the second unknown, we substitute 40 for xin the expression that represents
her score on the written part.

x 12  40  12

 52 This is her score on the written part.

State
Her score on the interview was 40 and her score on the written part was 52.

Check
Her score of 52 on the written exam was 12 points higher than her score of 40 on
the interview. Also, if we add the two scores, we get:

This is her combined score.

The results, 40 and 52, check.



40

 52

92

x 40

To isolate the variable x, divide both sides

(^) by 2 to undo the multiplication by 2.
2 x
2



80

2

2 x 80

2 x 12  12  92  12

2 x 12  92

xx 12  92

the overall

score.

is

the score on

the written part

plus

The score on

the interview

Self Check 7

CIVIL SERVICEA candidate for a

position with the IRS scored

15 points higher on the written

part of the civil service exam

than he did on his interview. If

his combined score was 155,

what were his scores on the

interview and on the written part?

Now TryProblem 25