Question

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

$\dfrac{1}{4}$

$\dfrac{1}{3}$

$\dfrac{3}{8}$

$\dfrac{2}{5}$

$\dfrac{1}{2}$

Solution:

After transferring half the coffee, cup $1$ has $2$ oz coffee and cup $2$ has $2$ oz coffee and $4$ oz cream, a total of $6$ oz.

Transferring half of cup $2$ back moves $1$ oz coffee and $2$ oz cream. Cup $1$ then holds $2 + 1 = 3$ oz coffee and $2$ oz cream.

The fraction that is cream is $\dfrac{2}{2+3} = \dfrac{2}{5}.$

Thus, the correct answer is D.

2002 AMC 12A Problem 10

Solution:

Problem 10 in Other Years