1998 AJHSME Problems/Problem 14

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Problem

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 both the Math Club and the Science Club.

These $12$ people are also $30\%$ of the Math Club.

Setting up a proportion:

$\frac{12}{30\%} = \frac{x}{100\%}$

$12\cdot 1.00 =0.30\cdot x$

$\frac{12}{0.3} = 40=x$

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

See also

1998 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 13
Followed by
Problem 15
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions

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