Question

A science class has four tests/ exams during the semester.

The final exam counts as two test scores. If your average after the first three tests is 76, what must you score on the final exam to reach a final test average of exactly 80?

Answer 1

86

Explanation:

You want to know the final grade required to bring your average up from 76 to 80, given that 76 is the average of 3 tests, and the final counts as two tests.

Average

If f is the score on your final exam, you want your ending grade to be ...

(3·76 +2·f)/5 = 80

228 +2f = 400 . . . . multiply by 5

114 +f = 200 . . . . . . divide by 2

f = 86 . . . . . . . . . . . subtract 114

Your final test score must be 86 to achieve an average of 80.

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Additional comment

Each of your three test grades is 4 points below the desired average, so a total of -12 relative to the average. The final test counts as 2 tests, so those must have a grade that totals 12 points above the desired average. That is, the final test must have a score of 80+(12/2) = 86.

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