Question

There are $42$ students in a class. $\frac{3}{4}$ of the boys and $\frac{2}{3}$ of the girls travel to school by bus. The total number of boys and girls who come to school by bus is $30.$ How many boys are there in the class $?$ How many girls come to school by bus $?$

Answer 1

Say the number of boys $=b$

and the number of girls $=g$

$\therefore$ $b+g=42$ (given) $⟶\left(1\right)$

Also

$\frac{3b}{4}+\frac{2g}{3}=30$ (given)

$\Rightarrow 9b+8g=360⟶\left(2\right)$

Substituting $g=42-b$ from equation $\left(1\right)$ in equation $\left(2\right)$ we get

$9b+8(42-b)=360$

$\Rightarrow 9b+336-8b=360$

$\Rightarrow b=24$

$\therefore$ $9=42-24=18$

$\therefore$ There are $24$ boys in the class and of the $30$ students those who travel by bus $\frac{2}{3}\times 18=12$ are girls.