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# The cost of 4 pens and 4 pencil boxes is Rs. 100. Three times the cost of a pen is Rs. 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.

Given:

The cost of 4 pens and 4 pencil boxes is Rs. 100. Three times the cost of a pen is Rs. 15 more than the cost of a pencil box.

To do:

We have to find the cost of a pen and a pencil box and form the pair of linear equations for the above situation.

Solution:Let the cost of a pen and a pencil box be $x$ and $y$ respectively.

According to the question,

$4x + 4y = 100$.....(i)

$3x = y+15$

$y=3x-15$.....(ii)

Substituting $y=3x-15$ in equation (i), we get,

$4x+4(3x-15)=100$

$4x+12x-60=100$

$16x=100+60$

$16x=160$

$x=\frac{160}{16}$

$x=10$

Substituting $x=10$ in equation (ii), we get,

$y=3(10)-15$

$y=30-15$

$y=15$

The cost of a pen is Rs. 10 and the cost of a pencil box is Rs. 15.

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