2012 AMC 12A Problem 4

Attempt Problem 4 of the 2012 AMC 12A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2012 AMC 12A solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

In a bag of marbles,

\dfrac{3}{5}

of the marbles are blue and the rest are red. If the number of red marbles is doubled and the number of blue marbles stays the same, what fraction of the marbles will be red?

\dfrac{2}{5}

\dfrac{3}{7}

\dfrac{4}{7}

\dfrac{3}{5}

\dfrac{4}{5}

Answer: C

Concepts:fraction ratio and proportion

Difficulty rating: 970

Small hint:

Start with a convenient total, such as

5

marbles

Big hint:

Blue and red begin at

3

and

2

; doubling the red gives

3

blue and

4

red

Solution:

Suppose there are

5

marbles:

3

blue and

2

red. Doubling the red gives

4

red while the blue stays at

3.

The total is now

3 + 4 = 7,

so the fraction that is red is

\dfrac{4}{7}.

Thus, the correct answer is C.