# 1994 AJHSME Problems/Problem 11

## Problem

Last summer $100$ students attended basketball camp. Of those attending, $52$ were boys and $48$ were girls. Also, $40$ students were from Jonas Middle School and $60$ were from Clay Middle School. Twenty of the girls were from Jonas Middle School. How many of the boys were from Clay Middle School? $\text{(A)}\ 20 \qquad \text{(B)}\ 32 \qquad \text{(C)}\ 40 \qquad \text{(D)}\ 48 \qquad \text{(E)}\ 52$

## Solution

Make a table with the information given. $$\begin{tabular}{c|ccc} & \text{Jonas} & \text{Clay} & \text{total} \\ \hline \text{boys} & & & 52 \\ \text{girls} & 20 & & 48 \\ \text{total} & 40 & 60 & 100 \end{tabular}$$

Because the first two columns must add up to the third column, and the same with the rows, the rest of the empty boxes can be filled in. $$\begin{tabular}{c|ccc} & \text{Jonas} & \text{Clay} & \text{total} \\ \hline \text{boys} & 20 & 32 & 52 \\ \text{girls} & 20 & 28 & 48 \\ \text{total} & 40 & 60 & 100 \end{tabular}$$

The number of boys from Clay is $\boxed{\text{(B)}\ 32}$.

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