2002 AMC 12A Problem 10

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 fraction

Difficulty rating: 1440

Small hint:

After the first transfer, cup

2

holds

2

oz coffee and

4

oz cream

Big hint:

Transferring back half of cup

2

moves its coffee and cream in equal proportion; find the cream in cup

1

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

Answer: D

Difficulty rating: 1440

Small hint:

Big hint:

Solution:

Problem 10 in other years