Question

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:ratio and proportion fraction

Difficulty rating: 870

Solution:

WLOG, let the number of marbles in the bag be $5.$ Since we only care about ratios, we can do this. Then there are $3$ blue marbles and $2$ red marbles.

Doubling the red marbles gives us $4$ of them. Then the fraction of red marbles is $\dfrac{4}{4 + 3} = \dfrac{4}{7}.$

Thus, C is the correct answer.

2012 AMC 10A Problem 7

Answer: C

Difficulty rating: 870

Solution:

Problem 7 in Other Years