90 children were at a picnic on the beach. 3/5 of the boys and 5/8 of the girls were swimming. If 35 children were not swimming, how many boys were swimming?

If we have b boys and g girls, we know that:

b+g = 90
35 kids not swimming means 55 kids swimming.

3/5 b + 5/8 g = 55
or
24b + 25 g = 2200
so,
24b + 25(90-b) = 2200
24b + 2250 - 25b = 2200
-b = -50
b=50
g=40

swimming were 30 boys and 25 girls = 55.