Question

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?

Answer 1

Boys = 150

Girls = 315

Total Boys and Girls 465

Explanation:

We call x the number of boys and we call y the number of girls.

So we have to find the total number of children

We know that

`(2)/(7)y = (3)/(5)x`

`x =y-165`

Now we substitute the second equation in the first and solve for y.

`(2)/(7)y = (3)/(5)(y-165)`

`(2)/(7)y = (3)/(5)y-99\\\\99 = (3)/(5)y-(2)/(7)y\\\\(11)/(35)y=99\\\\y = 315\\`

Now we find x.

`x = 315-165 = 150\\\\x = 150`

Finally we have that:

Boys = 150

Girls = 315

Total Boys and Girls 465