2002 AMC 12A Problems/Problem 10

Problem

Sarah places four ounces of coffee into an eight-ounce cup and four ounces of cream into a second cup of the same size. She then pours half the coffee from the first cup to the second and, after stirring thoroughly, pours half the liquid in the second cup back to the first. What fraction of the liquid in the first cup is now cream?

$\mathrm{(A) \ } \frac{1}{4}\qquad \mathrm{(B) \ } \frac13\qquad \mathrm{(C) \ } \frac38\qquad \mathrm{(D) \ } \frac25\qquad \mathrm{(E) \ } \frac12$

Solution

We take this problem step by step:

Step 0: We begin with 4 ounces of coffee in cup 1 and 4 ounces of cream in cup 2

Step 1: We now have 2 ounces of coffee in cup 1 and 4 ounces of cream and 2 ounces of coffee in cup 2.

Step 2: We now have $2+\frac22=3$ ounces of coffee and $\frac42=2$ of cream in cup 1 (and two ounces of cream and one of coffee in cup 2, though this does not matter).

So 2 out of the 5 ounces of liquid in cup 1 is cream, so the answer is $\frac25$ , or $\mathrm{D}$ .

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2002 AMC 12A Problems/Problem 10

Problem

Solution