Question

The cost of $1$ pencil and $3$ erasers is $Rs10$ and cost of $4$ pencils and $6$ erasers is $Rs28$. Find the cost of $5$ pencils and $4$ erasers.

Answer 1

Let $x$ be the number of pencils and $y$ be the number of erasers.

cost of $1$ pencil and $3$ erasers is $Rs.10\Rightarrow x+3y=10$

cost of $4$ pencils and $6$ erasers is $Rs.28\Rightarrow 4x+6y=28$ or $2x+3y=14$

Solving $x+3y=10$ and $2x+3y=14$ we get

$\Rightarrow 2x+3y-x-3y=14-10$

$\Rightarrow x=4$

$\therefore$Cost of $1$ pencil$=Rs.4$

Put $x=4$ in $x+3y=10$ we get

$4+3y=10\Rightarrow 3y=10-4=6$

$\therefore y=\frac{6}{3}=2$

$\therefore$Cost of $1$ eraser$=Rs.2$

Cost of $5$ pencils$=5\times 4=Rs.20$

Cost of $4$ erasers$=4\times 2=Rs.8$

Thus,cost of $5$ pencils and $4$ erasers$=5x+4y=5\times 4+4\times 2=20+8=Rs.28$