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
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
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1 answer