1988 AJHSME Problems/Problem 18

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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1988 AJHSME Problems/Problem 18

Problem

Solution

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