28. Sanvi purchased some books for 120. If she purchased 3 more books for
the same amount each book would have cost her 2 less. Find the number of books
purchased by Sanvi and the price of each book.
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Step-by-step explanation:
Let the no. of books purchased be x.
Price of book = ₹ 120 / x
According to given,
₹ 120/(x+3) = ₹ 120/x - ₹ 2
₹120/(x+3) = (₹120 - ₹2x)/x
₹120 × x = (₹120 - ₹2x) (x+3)
₹120x = ₹120x - ₹2x² + ₹360 - ₹6x
120x - 120x = -2x² - 6x + 360
0 = -2x² - 6x² + 360
-2( x² + 3x - 180 ) = 0
x² + 3x - 180 = 0/-2 = 0
x² + 15x - 12x - 180 = 0
x( x+15 ) -12 ( x+15 ) = 0
(x+15) (x-12) = 0
x + 15 = 0 OR x - 12 = 0
x = -15 OR x = 12
As x = No. of books, is a natural number, x > 0.
x = 12 books
Price of book = ₹120/x = ₹120/12 = ₹10
Ans :
No. of books = 12
Price of a book = ₹10
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