the cost of some books is rupees 60. cost of every book is the same.if the bookseller decreases the cost of any book by rs 1, one gets 5 book more for the same amount. what is the cost of each book and how many books are purchased?
Answers
Answer:
Each book costs Rs 4 and 15 books are purchased.
Step-by-step explanation:
Define x:
Let the number of books be x
Find the cost of 1 book:
Total cost of the books = Rs 60
Cost of 1 book = 60 ÷ x = 60/x
Find the new price if it decrease by Rs 1:
New Price = 60/x - 1
Solve x:
Cost of book decreased by Rs 1, number of purchase increased by 5
(60/x - 1)(x + 5) = 60
60 + 300/x - x - 5 = 60
300/x - x - 5 = 0
300 - x² - 5x = 0
x² + 5x - 300 = 0
(x - 15)(x + 20) = 0
x = 15 or x = -20 (rejected, since books purchased cannot be negative)
Find the number of books purchased:
Number of books = x = 15
Find the cost of a book:
Total cost = Rs 60
Number of books = 15
Cost of a book = 60 ÷ 15 = Rs 4
Answer: Each book costs Rs 4 and 15 books are purchased.
Answer:
The cost of each book is Rs 4 and total number of books purchased were 15.
Step-by-step explanation:
Let the cost of each book = x
Let number of books = y
Hence xy = 60
=> y = 60/x
After the price reduction new price = x-1
Total number of books = y + 5
Hence we get,
(x-1)(y+5) = 60
=> xy +5x - y -5 = 60
=> 60 + 5x - 60/x -5 = 60
=> 5x - 60/x -5 = 0
=> x -12/x - 1 = 0
=> x² - x -12 = 0
=> x = 4 or -3
rejecting -3 we get x = 4
=> y = 60/4 = 15
Hence the cost of each book is Rs 4 and total number of books purchased were 15