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?

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

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.