At the dance, the ratio of the number of girls to boys is 7:5. If there are 36 more girls than boys, how many girls were at the dance? How many boys were at the dance?

9514 1404 393

Step-by-step explanation:

The difference is 7-5 = 2 "ratio units", corresponding to a difference of 36 dancers. Then each "ratio unit" stands for 36/2 = 18 dancers.

There are 7×18 = 126 girls.

There are 5×18 = 90 boys.

You could solve this by writing some equations:

  g/b = 7/5

  g -b = 36

Then you could substitute for g:

  (36+b)/b = 7/5

  36/b +1 = 2/5 +1 . . . . expand the fractions

  36/b = 2/5 . . . . . . . . . subtract 1

  b = (5/2)(36) = 90 . . . multiply by 5/2b

  g = 36+90 = 126