# 1988 AJHSME Problems/Problem 18

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## Problem

The average weight of $6$ boys is $150$ pounds and the average weight of $4$ girls is $120$ pounds. The average weight of the $10$ children is $\text{(A)}\ 135\text{ pounds} \qquad \text{(B)}\ 137\text{ pounds} \qquad \text{(C)}\ 138\text{ pounds} \qquad \text{(D)}\ 140\text{ pounds} \qquad \text{(E)}\ 141\text{ pounds}$

## Solution

Let the $6$ boys have total weight $S_B$ and let the $4$ girls have total weight $S_G$. We are given \begin{align*} \frac{S_B}{6} &= 150 \\ \frac{S_G}{4} &= 120 \end{align*}

We want the average of the $10$ children, which is $$\frac{S_B+S_G}{10}$$ From the first two equations, we can determine that $S_B=900$ and $S_G=480$, so $S_B+S_G=1380$. Therefore, the average we desire is $$\frac{1380}{10}=138 \rightarrow \boxed{\text{C}}$$

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