At a festival, 2/7 of the number of girls was equal to 3/5 of the number of boys. There were 165 fewer boys then girls, how many children were at the festival in all?

We know this: 2/7 G = 3/5 B

We know this: B = (G - 165)

Plug the second equation into the first to solve for G: 2/7 G = 3/5 (G - 165)

Solve from there.

G = 315

Plug that into the second equation: B = (G - 165)

B = 315 - 165

B = 150

G + B = 465