2009 AMC 10A Problem 18

Below is the professionally curated solution for Problem 18 of the 2009 AMC 10A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2009 AMC 10A solutions, or check the answer key.

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Concepts:percentage Venn Diagram conditional probability

Difficulty rating: 1460

18.

At Jefferson Summer Camp, $60\%$ of the children play soccer, $30\%$ of the children swim, and $40\%$ of the soccer players swim. To the nearest whole percent, what percent of the non-swimmers play soccer?

$30\%$

$40\%$

$49\%$

$51\%$

$70\%$

Solution:

Take $100$ children: $60$ play soccer, and $40\%$ of them, or $24,$ also swim. So $60 - 24 = 36$ soccer players do not swim.

There are $30$ swimmers and $70$ non-swimmers, so the fraction of non-swimmers who play soccer is $\dfrac{36}{70} \approx 0.514 \approx 51\%.$

Thus, the correct answer is D.

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