5 pens and 6 pencils together cost ₹ 9 and 3 pens and 2 pencils cost ₹ 5. Find the cost of 1 pen and 1 pencil.

Given:

5 pens and 6 pencils together cost ₹ 9 and 3 pens and 2 pencils cost ₹ 5.

To do:

We have to find the cost of 1 pen and 1 pencil.

Let the cost of one pen and one pencil be $x$ and $y$ respectively.

According to the question,

$5x + 6y = 9$.....(i)

$3x + 2y = 5$.....(ii)

Multiplying equation (ii) by 3 on both sides, we get,

$3(3x+2y)=3(5)$

$9x+6y=15$.....(iii)

Subtracting equation (iii) from equation (i), we get,

$(9x+6y)-(5x+6y)=15-9$

$9x-5x+6y-6y=6$

$4x=6$

$x=\frac{6}{4}$

$x=\frac{3}{2}$

Substituting $x=\frac{3}{2}$ in equation (ii), we get,

$3(\frac{3}{2})+2y=5$

$\frac{9}{2}+2y=5$

$2y=5-\frac{9}{2}$

$2y=\frac{5\times2-9}{2}$

$2y=\frac{1}{2}$

$y=\frac{1}{2\times2}$

$y=\frac{1}{4}$

$x=1.5$ and $y=0.25$

The cost of a pen is Rs. 1.50 and the cost of a pencil is Rs. 0.25.

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Updated on: 10-Oct-2022

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