Fifteen children voted for their favorite color. the votes for red and blue together were double the votes for green and yellow together. how did the children vote?

We know that there are 15 children altogether 

We know that the number that voted for B+R is double the number of students voted for G+Y

B+R = 2(G+Y)

Think of two numbers that add up to 15, one number is twice of the other number. 

For example, 6 and 12.
12 is double of 6 but 6 + 12 doesn't give 15

So, think again

for example 5 and 10
10 is double of 5 and 5+10 does give 15

So, the number that voted Red and Blue is 10 and the number that voted Yellow and Green is 5

Looks pretty good to me!