Represent the following situations mathematically:A shopkeeper buys a

1.	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.
Answer» 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 ⇒ 80/(x + 4) = 80/x - 1 ⇒ 80x = (x + 4) (80 − x) ⇒ 80x = 80x − x² + 320 − 4x ⇒ x² + 4x + 320 = 0

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.

Answer»

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

⇒ 80/(x + 4) = 80/x - 1

⇒ 80x = (x + 4) (80 − x)

⇒ 80x = 80x − x² + 320 − 4x

⇒ x² + 4x + 320 = 0