Question

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

Answer 1

Find the two numbers.

The ratio of the numbers is $2:5$.

If the first integer is $2x$, the second integer must be $5x$.

The difference between the whole numbers is$66$.

The equation formed such that difference between the whole numbers is $66$ is as follows :

$5x-2x=66$

Solve the obtained equation:

$\begin{array}{rcl}5x-2x& =& 66\\ & \Rightarrow & 3x=66\\ & \Rightarrow & x=22\end{array}$

Put $x=22$ in $2x$ and $5x$ to find the integers:

$\begin{array}{rcl}2x& =& 2\times 22\\ & \Rightarrow & 2x=44\end{array}$

and

$\begin{array}{rcl}5x& =& 5\times 22\\ & \Rightarrow & 5x=110\end{array}$

So, the integers are $44\mathrm{and}110$.