1998 AJHSME Problems/Problem 14

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.

1998 AJHSME (Problems • Answer Key • Resources)
Preceded by 1997 AJHSME	Followed by 1999 AMC 8
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1998 AJHSME Problems/Problem 14

Problem 14

Solution

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