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2007 AMC 12B Problems/Problem 12

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Problem 12

A teacher gave a test to a class in which 10% of the students are juniors and 90% are seniors. The average score on the test was 84. The juniors all received the same score, and the average score of the seniors was 83. What score did each of the juniors receive on the test?

\mathrm {(A)} 85 \mathrm {(B)} 88 \mathrm {(C)} 93 \mathrm {(D)} 94 \mathrm {(E)} 98

Solution

Taking a weighted average

(90\%)(83) + (10\%)(x) = 84 where x is the Juniors' score

\begin{align*}x & = 10(84 - .9(83) \\& = 840 - 9(83) \\& = 93 \Rightarrow \mathrm {(C)}

See Also

2007 AMC 12B (ProblemsResources)
Preceded by
Problem 11
Followed by
Problem 13
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