SOLUTION: A sorority buys a case of sweatshirts for $480 to sell at a mixer. The sorority needs to sell all but 16 of the sweatshirts at a profit of $5 per sweatshirt to regain the $480 inve
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Question 1160413: A sorority buys a case of sweatshirts for $480 to sell at a mixer. The sorority needs to sell all but 16 of the sweatshirts at a profit of $5 per sweatshirt to regain the $480 investment. How many sweatshirts must be sold, and at what price, to do this?
_sweatshirts at $ _per sweatshirt Answer by ikleyn(52835) (Show Source):
Let "n" be the number of sweatshirts .
From the condition, you have this equation to find n
- = 5 dollars. (1)
Cancel the factor 5 in both sides
- = 1.
To solve the equation, multiply both sides by n*(n-16). You will get then
96n - 96*(n-16) = n*(n-16)
Simplify and reduce to the standard form quadratic equation
96n - 96n + 96*16 = n^2 - 16n
n^2 - 16n - 1536 = 0
n = = = .
The only positive root is n = = = 48.
ANSWER. n = 48 shirts.
CHECK. I will check equation (1): - = - = 15 - 10 = 5.
! Correct !
