5 books and 7 pens together cost ₹ 79 whereas 7 books and 5 pens together cost ₹ 77. Find the total cost of 1 book and 2 pens.


Given:

5 books and 7 pens together cost ₹ 79 whereas 7 books and 5 pens together cost ₹ 77.

To do:

We have to find the total cost of 1 book and 2 pens.

Solution:

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

According to the question,

$5x + 7y = 79$.....(i)

$7x + 5y = 77$.....(ii)

Multiplying equation (i) by 5 on both sides, we get,

$5(5x+7y)=5(79)$

$25x+35y=395$.....(iii)

Multiplying equation (ii) by 7 on both sides, we get,

$7(7x+5y)=7(77)$

$49x+35y=539$.....(iv)

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

$(49x+35y)-(25x+35y)=539-395$

$49x-25x+35y-35y=144$

$24x=144$

$x=\frac{144}{24}$

$x=6$

Substituting $x=6$ in equation (ii), we get,

$7(6)+5y=77$

$42+5y=77$

$5y=77-42$

$5y=35$

$y=\frac{35}{5}$

$y=7$

$\Rightarrow 2y=2(7)=14$

$x=6$ and $2y=14$

$x+2y=6+14=20$

The total cost of 1 book and 2 pens is Rs. 20.  

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Updated on: 10-Oct-2022

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