Question

$5$ pencils and $7$ pens together cost $Rs.50,$ whereas $7$ pencils and $5$ pens together cost $Rs.46.$ Find the costs of one pencil and one pen.

Answer 1

Let the cost of one pencil be ${}^{\prime }{x}^{\prime }$ and that of one pen be ${}^{\prime }{y}^{\prime }$

$5x+7y=50\dots \dots \left(i\right)$

$7x+5y=46\dots \dots \left(ii\right)$

On multiplying eq.(i) by 5 and eq.(ii) by 7, we get

$25x+35y=250\dots \dots \left(iii\right)$

$49x+35y=322\dots \dots \left(iv\right)$

On subtracting eq.(iii) from (iv), we get

$49x+35y-(25x+35y)=322-250$

$\Rightarrow 49x-25x=72$

$\Rightarrow 24x=72$

$\Rightarrow x=\frac{72}{24}=3$

On putting the value of $x$ in $eq.\left(i\right),$ we get

$\Rightarrow 5\times 3+7y=50$

$\Rightarrow 7y=50-15$

$\Rightarrow y=\frac{35}{7}=5$

Hence, the cost of one pencil is $Rs.3$ and one pen costs $Rs.5$