Question

A merchant purchased a number of coats, each at the same price, for a total of $720. He sold them at $40 each, thus realizing a profit equal to his cost of 8 coats. How many did he buy

Answer 1

number of coats --- n

purchase cost per coat = 720/n

total return = 40n
profit = 40n - 720

cost of 8 coats = 8(720/n)

40n - 720 = 8(720/n)
40n^2 - 720n - 5760 = 0
n2 - 18n - 144 = 0
(n - 24)(n + 6) = 0
n = 24 or n=-6, rejecting the negative

He bought 24 coats

check:
cost per coat = 720/24 = $30
cost of 8 coats = $240

profit on each coat = $10
total profit = 24(10) = $240
My answer is correct