Question

The difference between two positive integers is $30$. The ratio of these integers is $2:5$. Find the integers.

Answer 1

Find the integers.

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

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

The difference of the integers is$30$.

So, the equation for the difference is as follows:

$5x-2x=30$

Solve the obtained equation:

$\begin{array}{rcl}5x-2x& =& 30\\ & \Rightarrow & 3x=30\\ & \Rightarrow & x=10\end{array}$

Put $x=10$ in $2x$ and $5x$ to find the integers:

$\begin{array}{rcl}2x& =& 2\times 10\\ & \Rightarrow & 2x=20\end{array}$

and

$\begin{array}{rcl}5x& =& 5\times 10\\ & \Rightarrow & 5x=50\end{array}$

So, the integers are $20\mathrm{and}50$.