Question

$5$ pens and $6$ pencils together cost $Rs.37$ and $3$ pens and $3$ pencils together cost $Rs.21$. Find the cost of a pen and a pencil.

Answer 1

Let x and y be cost of a pen and a pencil respectively.
Then according to question,
$5x+6y=37$ ...(i)
$3x+3y=21\Rightarrow x+y=7$ ...(ii)
from (ii) $y=7-x$
from (i)
$5x+6(7-x)=37$
$\Rightarrow 5x+42-6x=37$
$\Rightarrow x=5$
$\Rightarrow y=7-5=2$
cost of a pen$=Rs.5$
cost of a pen$=Rs.2$