Question

The sum of two numbers exceeds thrice the smaller by $3$. If the difference between them is $5$, find the numbers

Answer 1

Let the larger number be $x$ and the smaller be $y$.

Then the first condition says $x+y-3y=3$.

The second condition gives $x-y=5$.

Thus we get two equations
$x-2y=3$ .... (1)
$x-y=5$ .... (2)
Subtracting the equation (2) by (1), we get $-y=-2$.

Hence $y=2$.

This gives $x=y+5=2+5=7$.
Thus the larger number is $7$ and the smaller is $2$.