Question

The different between two whole numbers is $66$. The ratio of the the numbers is $2:5$. What are the two numbers?

Answer 1

$\begin{array}{c}Twowholenumbersx,y\\ x-y=66\to \left(i\right)\\ \frac{y}{x}=\frac{2}{5}\\ 5y=2x\\ 2x-5y=0\to \left(ii\right)\\ \left(2\right)-\left(1\right)\times 2\\ 2x-5y=0\\ 2x-2y=66\times 2\\ -+-\\ \overline{+3y=132}\\ y=44\\ putvalueofyin\left(i\right)\\ x-44=66\\ x=44+66\\ =110\\ number=110,44\end{array}$