2012 AMC 12A Problem 4

Below is the professionally curated solution for Problem 4 of the 2012 AMC 12A, 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.

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Concepts:fractionratio and proportion

Difficulty rating: 970

4.

In a bag of marbles, 35\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?

25\dfrac{2}{5}

37\dfrac{3}{7}

47\dfrac{4}{7}

35\dfrac{3}{5}

45\dfrac{4}{5}

Solution:

Suppose there are 55 marbles: 33 blue and 22 red. Doubling the red gives 44 red while the blue stays at 3.3.

The total is now 3+4=7,3 + 4 = 7, so the fraction that is red is 47.\dfrac{4}{7}.

Thus, the correct answer is C.

Problem 4 in Other Years