Question

The sum of two numbers is $35$. Four times the larger number is $5$ more than $5$ times the smaller number. Find these numbers.

Answer 1

Let the two numbers are x and y , such that $x>Y$ , then

$4y=5x+5....\left(1\right)$

also , $x+y=35$

$\Rightarrow y=35-x.....\left(2\right)$

putting the value of $y$ from $\left(2\right)$ in $\left(1\right)$

$4\left(35-x\right)=5x+5$

$\Rightarrow 140-4x=5x+5$

$\Rightarrow 9x=135$

$\Rightarrow x=15$

from $\left(1\right)$

$4y=5x+5$

$\Rightarrow 4y=5\times 15+5$

$\Rightarrow 4y=80$

$\Rightarrow y=20$

So , the required numbers are $15$ and $20$