Question

The difference between two numbers is $4$. If the sum of five times the smaller number and bigger number is $58$, find the numbers.

Answer 1

Let $x$ and $y$ be the two numbers such that $x>y$.

$x-y=4.....\left(1\right)$

Also,

$5y+x=58.....\left(2\right)$

Subtracting equation $\left(1\right)$ from $\left(2\right)$, we have

$(5y+x)-(x-y)=58-4$

$6y=54$

$\Rightarrow y=\frac{54}{6}=9$

$\therefore x-9=4\Rightarrow x=9+4=13$

Hence the two numbers are $9$ and $13$.