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 \[\frac{1380}{10}=138 \rightarrow \boxed{\text{C}}\]

See Also

1988 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 17
Followed by
Problem 19
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All AJHSME/AMC 8 Problems and Solutions

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