Question

The sum of two positive numbers $x$ and $y(x>y)$ is $50$ and the difference of their squares is $720$. Find the numbers.

Answer 1

Given,

$x$ and $y$ are two positive integers.

Sum of the two positive integers is $50$.

$\Rightarrow x+y=50$.............(1)

The difference of their squares is &720$.

$\Rightarrow x^2-y^2=720$...................(2)

$\Rightarrow (x-y)(x+y)=720$

$\Rightarrow (x-y)\left(50\right)=720$

$\Rightarrow (x-y)=\frac{720}{50}$

$\Rightarrow x-y=\frac{72}{5}$............(3)

$\left(1\right)+\left(3\right)$

$x+y+x-y=50+\frac{720}{50}$

$\Rightarrow 2x=50+\frac{72}{5}$

$\Rightarrow 2x=\frac{322}{5}$

$\Rightarrow x=\frac{322}{10}$

$\Rightarrow x=32.2$

From (1)

$x+y=50$

$\Rightarrow y=50-32.2=17.8$

$x=32.2$ and $y=17.8$ are required numbers.