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

Answer

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Hint:In order to solve these types of questions, firstly we have to convert the statements into equations by which we get two equations and after solving these equations we will get the cost of $1$ pen and $1$ pencil.

Complete step-by-step answer:

Assuming,

The cost of a pen be $Rs.x$ and that of pencil be $Rs.y$

We have given that, cost of $5$ pen and $6$ pencils together cost $Rs.9$

Therefore,

$5x + 6y = 9 - - - - - - \left( 1 \right)$

And the cost of $3$ pens and 2 pencils cost $Rs.5$.

Thus,

$3x + 2y = 5 - - - - - - \left( 2 \right)$

Multiplying equation (1) by 2 and equation (2) by 6, we get

$10x + 12y = 18 - - - - - \left( 3 \right)$

$18x + 12y = 30 - - - - - \left( 4 \right)$

Subtracting equation (3) by equation (4), we get

$18x - 10x + 12y - 12y = 30 - 18$

Or $8x = 12$

Or $x = \dfrac{3}{2}$

Or $x = 1.5$

Substituting $x = 1.5$

In equation (1), we get

$5 \times 1.5 + 6y = 9$

Or $7.5 + 6y = 9$

Or $6y = 9 - 7.5$

Or $6y = 1.5$

Or $y = \dfrac{{1.5}}{6}$

Or $y = \dfrac{1}{4}$

Or $y = 0.25$

Hence, the cost of one pen $ = Rs1.50$ and the cost of one pencil $ = Rs0.25$ .

Note: Whenever we face such a type of question simply we have to assume the cost Assume the cost of a pen be $Rs.x$ and that of pencil be $Rs.y$ after then we have to solve the equations by adding or subtracting equations to get our desired answer.

Complete step-by-step answer:

Assuming,

The cost of a pen be $Rs.x$ and that of pencil be $Rs.y$

We have given that, cost of $5$ pen and $6$ pencils together cost $Rs.9$

Therefore,

$5x + 6y = 9 - - - - - - \left( 1 \right)$

And the cost of $3$ pens and 2 pencils cost $Rs.5$.

Thus,

$3x + 2y = 5 - - - - - - \left( 2 \right)$

Multiplying equation (1) by 2 and equation (2) by 6, we get

$10x + 12y = 18 - - - - - \left( 3 \right)$

$18x + 12y = 30 - - - - - \left( 4 \right)$

Subtracting equation (3) by equation (4), we get

$18x - 10x + 12y - 12y = 30 - 18$

Or $8x = 12$

Or $x = \dfrac{3}{2}$

Or $x = 1.5$

Substituting $x = 1.5$

In equation (1), we get

$5 \times 1.5 + 6y = 9$

Or $7.5 + 6y = 9$

Or $6y = 9 - 7.5$

Or $6y = 1.5$

Or $y = \dfrac{{1.5}}{6}$

Or $y = \dfrac{1}{4}$

Or $y = 0.25$

Hence, the cost of one pen $ = Rs1.50$ and the cost of one pencil $ = Rs0.25$ .

Note: Whenever we face such a type of question simply we have to assume the cost Assume the cost of a pen be $Rs.x$ and that of pencil be $Rs.y$ after then we have to solve the equations by adding or subtracting equations to get our desired answer.

Last updated date: 16th Sep 2023

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