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.

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#### Solution

Let the cost of a book be Rs x and that of a pen be Rs y. Then,

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

7x + 5y = 77 ....(iii)

Multiplying equation (i) by 5 and equation (ii) by 7, we get

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

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

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

49x - 25x = 539 - 395

=> 24x = 144

`=> x = 144/24 = 6`

∴ Cost of a book = Rs 6

Putting x = 6 in equation (i), we get

5 x 6 + 7y = 79

=> 30 + 7y = 79

=> 7y = 769 - 30

=> 7y = 49

`=> y = 79/7 = 7`

∴Cost of a pen = Rs 7

∴ Cost of 2 pens = 2 x 7 = Rs 14

Hence, the total cost of 1 book and 2 pens = 6 + 14 = Rs 20

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