2002 AMC 10A Problems/Problem 17

Problem

Sarah pours 4 ounces of coffee into a cup that can hold 8 ounces. Then she pours 4 ounces of butter into a second cup that can also hold 8 ounces. She then pours half of the contents of the first cup into the second cup, completely mixes the contents of the second cup, then pours half of the contents of the second cup back into the first cup. What fraction of the contents in the first cup is butter?

$\text{(A)}\ 1/4 \qquad \text{(B)}\ 1/3 \qquad \text{(C)}\ 3/8 \qquad \text{(D)}\ 2/5 \qquad \text{(E)} 1/2$

Solution

After the first step, there are 2 ounces coffee in the first cup, and 4 ounces of butter plus 2 ounces of coffee in the second cup. When half of the second cup is poured into the first, there are $2+1=3$ ounces of coffee and 2 ounces of butter. Hence, our ratio is $\boxed{\frac{2}{5}\Rightarrow \text{(D)}}$ .

2002 AMC 10A (Problems • Answer Key • Resources)
Preceded by Problem 16	Followed by Problem 18
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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2002 AMC 10A Problems/Problem 17

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