Question

$5$ pencils and $7$ pens together cost $Rs50$, whereas $7$ pencils and $5$ pens together cost $Rs46$. Find the cost of one pencil and that of one pen.

Answer 1

Let the cost of a pencil be $x$ and cost of one pen be $y$.

$\Rightarrow$$5x+7y=\mathrm{50.......}\left(1\right)$

$\Rightarrow$$7x+5y=\mathrm{46.......}\left(2\right)$

Adding and subtracting (1) and (2)

$\Rightarrow$$2x-2y=-4$

$\Rightarrow$$12x+12y=96$

$\Rightarrow$$x-y=-\mathrm{2.........}\left(3\right)$

$\Rightarrow$$x+y=\mathrm{8...........}\left(4\right)$

Add $\left(3\right)$ and $\left(4\right)$

$\Rightarrow$$2x=6$

$\Rightarrow$$x=3$

$\Rightarrow$$3-y=-2$

$\Rightarrow$$y=5$

cost of one pencil=$Rs3$

cost of one pen=$Rs5$