1998 AMC 8 Problem 14

Below is the professionally curated solution for Problem 14 of the 1998 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1998 AMC 8 solutions, or check the answer key.

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Concepts:percentage

Difficulty rating: 1180

14.

At 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?

$12$

$15$

$30$

$36$

$40$

Solution:

Since $80\%$ of people are in both clubs, the number of people in both clubs is $0.8\cdot 15=12.$ This is $30\%$ of the math club, so the number of people in the math club is $\dfrac{12}{0.3}=40.$

Thus, the correct answer is E .

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