2002 AMC 10A Problem 17

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}

Answer: D

Concepts:mixture process simulation

Difficulty rating: 1450

Small hint:

Track ounces of coffee and cream after each transfer

Big hint:

The second cup is uniformly mixed before the second transfer

Solution:

After transferring

2

oz of coffee, cup

1

has

2

oz coffee and cup

2

has

2

oz coffee plus

4

oz cream, a total of

6

oz.

Transferring back half of cup

2

(that is

3

oz, consisting of

1

oz coffee and

2

oz cream) leaves cup

1

with

3