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2009 AMC 10A Problem 18

2009 AMC 10A Problem 18AMC 10 Step by Step

Name: Date: September 13, 2026

Ratios, Percents & Averages · difficulty 3 of 5 · about 3 min · position P16-20

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?

A)
$30\%$
B)
$40\%$
C)
$49\%$
D)
$51\%$
E)
$70\%$

Answer

Key insight

Take 100 children: 60 play soccer, 24 of them swim, so 36 soccer players don't swim, out of 70 non-swimmers: 36/70 = 51%.

Solution

Since only percentages are involved, assume there are $100$ children.

Soccer players: $60$ .
Swimmers: $30$ , so non-swimmers: $70$ .
Soccer players who swim: $40\%$ of $60 = 24$ .
Soccer players who do not swim: $60 - 24 = 36$ .

The question asks what fraction of the $70$ non-swimmers play soccer:
$\frac{36}{70} = \frac{18}{35} \approx 0.514,$
which rounds to $51\%$ .

The answer is $\boxed{\textbf{(D)}\ 51\%}$ .

Why this works

Two overlapping categories (soccer, swimming) form a $2 \times 2$ table; the given data fill in the soccer row and the swim column, and the overlap ( $24$ ) determines every other cell. The phrase "percent of the non-swimmers" fixes the denominator: it is the size of the group being described, not the whole camp.

The trap

Taking 40% of the 30 swimmers instead of 40% of the 60 soccer players, or dividing the 36 by 100 rather than by the 70 non-swimmers.

Common mistakes

Taking 40% of the 30 swimmers instead of 40% of the 60 soccer players, or dividing the 36 by 100 rather than by the 70 non-swimmers.
Rounding $36/70$ carelessly to $50\%$ and then choosing $49\%$ ; the exact value $51.4\%$ rounds up.

Techniques

Test small/specific values or special cases to find or verify the answer