1998 AJHSME Problems/Problem 14

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Problem 14

An Annville Junior High School, $30\%$ of the students in the Math Club are in the Science Club, and $80\%$ of the students in the Science Club are in the Math Club. There are 15 students in the Science Club. How many students are in the Math Club?

$\text{(A)}\ 12 \qquad \text{(B)}\ 15 \qquad \text{(C)}\ 30 \qquad \text{(D)}\ 36 \qquad \text{(E)}\ 40$


Solution

If $80\%$ of the people in the science club of $15$ people are in the Math Club, $\frac{4}{5}\times15=12$ people are in the Math Club who is in the Science Club.

$12$ is also $30\%$ compared to how many people are in the Math Club.

$12=30\%$

$4=10\%$

$40=100\%$

There are $40=\boxed{E}$ people in the Math Club.


See also

1998 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 13
Followed by
Problem 15
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All AJHSME/AMC 8 Problems and Solutions