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

Question:

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

Solution:

Given:

(i) Cost of 5 books and 7 pens = Rs. 79.

(ii) Cost of 7 books and 5 pens = Rs. 77.

To find: Cost of 1 book and 2 pens.

Suppose the cost of 1 book = Rs x.

and the cost of 1 pen = Rs y.

According to the given conditions, we have

5x + 7y = 79

5x + 7y − 79 = 0 …… (1)

7x + 5y = 77,

5x + 7y − 77 = 0 …… (2)

Thus we get the following system of linear equation,

$5 x+7 y-79=0$ and

$5 x+7 y-77=0$

$\frac{x}{-539+385}=\frac{-y}{-385+553}=\frac{1}{25-49}$

$\frac{x}{-144}=\frac{-y}{-168}=\frac{1}{-24}$

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

$x=6$

$\frac{-y}{-385+553}=\frac{1}{25-49}$

$\frac{-y}{168}=\frac{1}{-24}$

$y=\frac{-168}{-24}$

$y=7$

Hence, the cost of 1 book = Rs 6

and the cost of 1 pen = Rs 7.

Therefore the cost of 2 pen = Rs 14.

Total cost of 1 book and 2 pens = 14 + 6 = 20

Total cost of 1 book and 2 pens $=$ Rs. 20

Hence total cost of 1 book and 2 pens $=$ Rs. 20