# 2007 AMC 10B Problems/Problem 16

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The following problem is from both the 2007 AMC 10B #16 and 2007 AMC 12B #12, so both problems redirect to this page.

## Problem

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? $\textbf{(A) } 85 \qquad\textbf{(B) } 88 \qquad\textbf{(C) } 93 \qquad\textbf{(D) } 94 \qquad\textbf{(E) } 98$

## Solution

We can assume there are $10$ people in the class. Then there will be $1$ junior and $9$ seniors. The sum of everyone's scores is $10 \cdot 84 = 840.$ Since the average score of the seniors was $83,$ the sum of all the senior's scores is $9 \cdot 83 = 747.$ The only score that has not been added to that is the junior's score, which is $840 - 747 = \boxed{\mathrm{(C) \ } 93}$

## Solution 2

Let the average score of the juniors be $j$. The problem states the average score of the seniors is $83$. The equation for the average score of the class (juniors and seniors combined) is $\frac{j}{10} + \frac{83 \cdot 9}{10} = 84$. Simplifying this equation yields $j = \boxed{\mathrm{(C) \ } 93}$

~mobius247

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 