2004 AMC 10B Problem 14

Problem 14 of 25IntermediateArithmetic

A bag initially contains red marbles and blue marbles only, with more blue than red. Red marbles are added to the bag until only

\tfrac{1}{3}

of the marbles in the bag are blue. Then yellow marbles are added to the bag until only

\tfrac{1}{5}

of the marbles in the bag are blue. Finally, the number of blue marbles in the bag is doubled. What fraction of the marbles now in the bag are blue?

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Solution

Let there be

B

blue marbles. After adding red marbles the total is

3B;

after adding yellow marbles the total is

5B,

still with

B

blue. Doubling the blue marbles gives

2B

blue out of

6B

total, which is

\dfrac{2B}{6B} = \dfrac{1}{3}.

Thus, the correct answer is C.

Tagged: fraction · ratio and proportion