# The ratio of girls to boys is 2:3 and there are 20 people in the class, how many are girls and boys?

Jun 2, 2015

Lets name $b$ the number of boys and $g$ the number of girls
$b + g = 20$
$\frac{g}{b} = \frac{2}{3}$ so $g = \frac{2 b}{3}$ ( we multiply by $b$ on each side )

We can thus replace g in the equation :

$b + \frac{2 b}{3} = 20$

We want to put on the same denominator :

$\frac{3 b}{3} + \frac{2 b}{3} = 20$

$\frac{5 b}{3} = 20$

$5 b = 60$ ( we multiply by $3$ on each side )
$b = 12$ ( we divide by $5$ on each side )

We can thus now find $g$ :

$b + g = 20$
$12 + g = 20$
$g = 20 - 12$ ( we substract $12$ on each side )
$g = 8$

There are thus $12$ boys and $8$ girls in the class