Civil Service

(1) 40

(2) 52

Explanation

Analyze

• The 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 x = her 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 higher on the written part than on the interview

Translation: add 12 points to the interview score

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

• (The score on the interview) plus (the score on the written part) is (the overall score)
• x + x + 12 = 92

Solve

• We need to isolate x on the left side
  • x + x + 12 = 92
• On the left side, combine like terms: x + x = 2x
  • 2x + 12 = 92
• To isolate the variable term, 2x, subtract 12 from both sides to undo the addition of 12
  • 2x + 12 - 12 = 92 - 12
• Do the subtraction
  • 2x = 80
• To isolate the variable x, divide both sides by 2 to undo the multiplication by 2
  • \(\frac{2x}{2} = \frac{80}{2}\)
• Do the division
  • x = 40

To find the second unknown, we substitute 40 for x in 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:

40 + 52 = 92

The result, 40 and 52, check