Question

One number is greater than thrice the other number by $2$ and $4$ times smaller number exceeds greater number by $5$.Find the numbers.

Answer 1

Let the greater number be $x$ and smaller number be $y$

Then, according to the given conditions, we have

$x-3y=2,$

$4y-x=5$

Thus, we have $x-3y=2$ ........$\left(1\right)$

$-x+4y=5$ .......$\left(2\right)$

Adding $\left(1\right)$ and $\left(2\right)$ we get

$x-3y-x+4y=2+5$

$\Rightarrow y=7$

Put $y=7$ in $\left(1\right)$ we get

$x-3y=2$

$\Rightarrow x-3\times 7=2$

$\Rightarrow x-21=2$

$\Rightarrow x=2+21=23$

$\therefore$ Greater number$=23$ and smaller number $=7$