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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)}\ 14...

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 (ProblemsResources)
Preceded by
Problem 17
Followed by
Problem 19
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Want to learn how to tackle those tough MATHCOUNTS and AMC counting and probability problems? Check out Art of Problem Solving's Introduction to Counting & Probability by David Patrick.
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