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.