What fraction of the marbles will be red?

Question

In a bag of marbles, 3/5 of them are blue and the rest are red. If the number of red marbles are doubled and the blue stays the same..

Answer 1

Blue = 3/5 (6/10) so Red = 2/5 (4/10).

 

Double the red to 4/5 (8/10) and the blue stay the same.

 

We've added 4 more Red marbles to the mix so now the denominator numbers are out of 14 instead of 10.

 

Blue = 3/7 (6/14)  and Red = 4/7 (8/14).

 

4/7 should be the answer.

Answer 2

For this problem, use a concrete number of marbles that fit the criteria.  Let's use 3 blue and 2 red marbles.  So there are 5 marbles, 3/5 of which are blue, and 2/5 of which are red.  Now double the red marbles to 4.  Now you have 4 red marbles and 3 blue marbles.  So your new ratio will be 4/7.

 

This is done by adding 2 to both the numerator and denominator:  (2+2) / (5+2) = 4/7

Incidentally, the new fraction for blue marbles is 3/7.

I hope that helps.