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 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.

1998 AJHSME (Problems • Answer Key • Resources)
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
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1998 AJHSME Problems/Problem 14

Problem 14

Solution

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