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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.