Question

Candace had scores of 94, 83, 92, and 86 on her first four exams of the semester. What score must she obtain on the fifth exam to have an average of 90 or better for the five exams?

Answer 1

95

Explanation:

The total of deviations from average must be zero.

deviations

(94 -90) = 4

(83 -90) = -7

(92 -90) = 2

(86 -90) = -4

and for the 5th exam:

(x -90) . . . . where the exam score is x

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total of deviations

We want the sum to be zero:

4 -7 +2 -4 +(x -90) = 0

x -95 = 0 . . . . . . . simplify

x = 95 . . . . . . . . . add 95

Candace must get a 95 or better to have an average of 90 for the 5 exams.

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Additional comment

When we're figuring this out mentally, we observe that 4 and -4 cancel, so Candace needs 5 more points than average to balance the net -5 she has from (-7+2). That is, she needs 90+5 = 95.

For many problems involving averages or sequences of numbers, it is often convenient to look at the deviations from average.

Answer 2

A score of 95 she must obtain on the fifth exam to have an average of 90 or better for the five exams

Explanation:

average = sum of all terms / number of terms

average = 94 + 83 + 92 + 86 + x / 5

90 = 355 + x / 5

multiply both sides by 5,

90 * 5 = 355 + x / 5 * 5

450 = 355 + x

subtract 355 from both sides to get x alone

450 - 355 = 355 + x - 355

95 = x