Question

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?

$\dfrac{1}{5}$

$\dfrac{1}{4}$

$\dfrac{1}{3}$

$\dfrac{2}{5}$

$\dfrac{1}{2}$

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.

2004 AMC 10B Problem 14

Solution:

Problem 14 in Other Years