Question

The cost of $4$ pens and $4$ pencil boxes is $₹100$. Three times the cost of a pen is $₹15$ more than the cost of a pencil box. Form the pair of linear equations for the above situation. Find the cost of a pen and a pencil box.

Answer 1

Given

The cost of pens and $4$ pencil boxes $=₹100$

Three times the cost of a pen is $₹15$ more than the cost of a pencil box.

We have to determine the cost of a pen and a pencil box.

Let the cost of a pen and a pencil box be $₹x$ and respectively.

According to the given data, we get to know that

$4x+4y=100$

Or $x+y=25$ …….$\left(i\right)$

$3x=y+15$

Or $3x-y=15$……….$\left(ii\right)$

On adding Equation $\left(i\right)$ and $\left(ii\right)$, we get,

$4x=40$

So, $x=10$

Substituting $x=10$, in Eq. $\left(i\right)$ we get

$$\begin{gathered} y=25-10 \\ =15 \end{gathered}$$

Answer

Hence, the cost of a pen $=₹10$

The cost of a pencil box$=₹15$