Question

The cost of $1$ pencil and $3$ erasers is Rs.$10$ and the cost of $4$ pencils and $6$ erasers is $Rs.28$.Find the cost of $5$ pencils and $4$ erasers.

Answer 1

Let $x$ and $y$ be the cost of $1$ pencil and $1$ eraser respectively.

According to the question-

$x+3y=10.....\left(1\right)$

$4x+6y=28$

$\Rightarrow 2x+3y=14.....\left(2\right)$

Subtracting equation $\left(1\right)$ from $\left(2\right)$, e have

$(2x+3y)-(x+3y)=14-10$

$2x+3y-x-3y=4$

$x=4$

Subsituting the value of $x$ in equation $\left(1\right)$, we have

$4+3y=10$

$\Rightarrow 3y=6$

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

Hence the cost of $1$ pencil and $1$ eraser respectively is $Rs.4$ and $Rs.2$ respectively.

Now,

Cost of $5$ pencils and $4$ erasers $=5x+4y=(5\times 4)+(4\times 2)=20+8=28$

Hence the cost of $5$ pencils and $4$ erasers is $Rs.28$.