Question

Divide $32$ into two parts such that $5$ times one part added to $6$ times the other part gives $164$

Answer 1

Let $32$ be divided into $x$ and $y$, i.e.,

$x+y=32.....\left(1\right)$

Also, given that

$5x+6y=164$

$\Rightarrow 5x+5y+y=164$

$\Rightarrow 5(x+y)+y=164$

$\Rightarrow 5\cdot 32+y=164\left(\text{From}\left(1\right)\right)$

$\Rightarrow y=164-160=4$

Substituting the value of $y$ in equation $\left(1\right)$, we have

$x+4=32$

$\Rightarrow x=32-4=28$

Hence $32$ is divided into $4$ and $28$.