Question

Divide 72 in a ratio of 3:5

Answer 1

The ratio is 3:5.
$\frac{x}{y}=\frac{3}{5} \ \ \ |\hbox{cross multiply} \\ 5x=3y \ \ \ |\div 5 \\ x=\frac{3}{5}y$

You have to divide 72, so the sum of x and y is 72.
$x+y=72 \ \ \ |-y \\ x=72-y$

Set both expressions equal to each other:
$x=x \\ \frac{3}{5}y=72-y \ \ \ |\times 5 \\ 3y=360-5y \ \ \ |+5y \\ 8y=360 \ \ \ |\div 8 \\ y=45 \\ \\ x=72-y=72-45=27$

72 divided in a ratio of 3:5 is 27:45.