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 than girls, how many children were at the festival in all?

X=number of girls.

y=number of boys.

We can suggest this system of equations:

2/7 x=3/5 y ⇒10x=21y ⇒x=21/10 y

y=x-165

We can solve this problem by substitution method:

x = (21/10) (x-165)

10x=21x-3465

10x-21x=-3465

-11x=-3465

x=-3465 / - 11=315

y=x-165=315-165=150

Number of children=number of girls + number of boys

Number of children=315 + 150=465

Answer: there were 465 children at the festival.