Tico's scores on four tests are 83,91,78, and 81. How many points above his current average must Tico score on the next test in order to raise his average 2 points?

Answer 1

Tico's scores on four tests are 83,91,78, and 81. How many points above his current average must Tico score on the next test in order to raise his average 2 points?

Test scores are averaged arithmetically. That means the test scores are all added together then divided by the number of tests.

His current average is:

(1/4)(83 + 91 + 78 + 81) = 83.25

I choose to carry the fraction through the rest of the problem.

Let S represent the score he must get on the fifth exam. Then we do this:

(1/5)(83 + 91 + 78 + 81 + S) = 83.25 + 2=85.25

Multiply both sides by 5:

5(1/5)(83 + 91 + 78 + 81 + S) = 5(83.25)

83 + 91 + 78 + 81 + S = 426.25

S = 426.25 - 83 - 91 - 78 - 81

S = 93.25

He must score a 94 on the fifth exam.