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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
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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