There are 12 boys and 10 girls in your gym +6 boys joined at the class how many girls would need to join for the ratio of boys to girls and the remainder same

So before, the ratio was 10/12.
First thing is to reduce that as much as possible to get 5/6
If you add 6 boys to the current twelve, you get x/18

So that means that 5/6 = x/18

To make those equal you can cross multiply OR, as an easier way, notice how 6 * 3 = 18? so that means all you have to do to get the denominators to be the same is to do 5/6 * 3

(6*3=18 & 5*3=15)
So that means that x = 15

The correct ratio is 15/18