Question

The sum of two numbers is $55$ and their difference is $7.$ Find the numbers.

Answer 1

Let the two numbers be x and y, where x > y
By the given data, $x+y=55$ ........ (1)
$x-y=7$ .......... (2)
Equation (2) becomes, $x=7+y$ ......... (3)
Substituting x in (1) we get, $7+y+y=55$
$\Rightarrow 2y=55-7=48$
$\therefore y=\frac{48}{2}=24$
Substituting y = 24 in (3) we get, $x=7+24=31$.
$\therefore$ The required two numbers are 31 and 24.