Q3 of 168 Page 7

Represent the following situations mathematically:

A shopkeeper buys a number of books for Rs. 80. If he had bought four more books for the same amount, the book would have cost Re. 1 less.

Let ‘x’ be the number of books bought by the shopkeeper.

∴ Cost of one book = Rs. 80 ÷ x.


[∵ the total cost of books is Rs. 80]


∴ Cost of one book when he buys 4 more books for same rate = Rs. 80 ÷ (x + 4).


When he buys four more books for the same amount; it will cost Re. 1 per book less than the previous.


∴ 80 ÷ (x + 4) = (80 ÷ x) − 1


⇒


⇒ 80x = (x + 4) (80 − x)


⇒ 80x = 80x − x2 + 320 − 4x


⇒ x2 + 4x + 320 = 0


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