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

there were 465 children  at the festival.