There are 12 boys and 10 girls in your gym class. if 6 boys joined the class, how many girls would need to join for the ratio of boys to girls to remain the same?

Number of boys in the gym class = 12
Number of girls in the gym class = 10
then
Ratio of boys to ratio of girls = 12:10
                                               = 6:5
Now
Number of boys joining the gym class later = 6
So after the new boys join the number of boys in the gym class becomes = 18
The ratio of boys to girls have to remain the same
Let us assume that the number of girls that need to join the gym class = x
Then
6/5 = 18/(x + 10)
6(x + 10) = 18 * 5
6x + 60 = 90
6x = 90 - 60
6x = 30
x = 30/6
   = 5
So the number of girls that need to join the gym class to keep the ratio same is 5. I hope the procedure is clear enough for you to understand.

So 12 and 10
if 6 boys joined then it is now
12+6=18
so we now need to have
12:10=18:x
solve for x
convert to fraction
12/10=18/x
multiply both sides by x
12x/10=18
multiply both sides by 10
12x=180
divide both sides by 12
x=15
so from 10 to 15 is a difference of 5 so 5 girls need to join

the answe ris 5