Tuesday, June 2, 2020

06/02/2020 (2019: AMC 8, Problem 7)

Q: Shauna takes five tests, each worth a maximum of 100 points. Her scores on the first three tests are 76, 94, and 87. In order to average 81 for all five tests, what is the lowest score she could earn on one of the other two tests?

$\textbf{(A) }48\qquad\textbf{(B) }52\qquad\textbf{(C) }66\qquad\textbf{(D) }70\qquad\textbf{(E) }74$

If Shauna averages 81 on 5 tests, that means she would have 81 ⋅ 5 = 405 total points.

Because we know that she got a 76, 94, and 87 on 3 tests, we can subtract them from 405 to see what the sum of the other two tests' scores is. 405 - (76 + 94 + 87) = 148.

The highest she can get on one test is 100, making the lowest score that she could earn on one of the other two tests 148 - 100 = 48. That makes the answer A.

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