SOLUTION: How would one go about writing 48/n(n-2)+22 as a quadratic equation? I'm working on the problem: A retailer spent $48 to purchase a number of special mugs. Two of them were broke

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Question 436995: How would one go about writing 48/n(n-2)+22 as a quadratic equation?
I'm working on the problem:
A retailer spent $48 to purchase a number of special mugs. Two of them were broken in the store, but by selling each of the remaining mugs for $3 above the original cost per mug, she made a total profit of $22.
Construct an equation that will allow us to solve for the number of mugs, denoted by n, that were originally purchased.
Just by looking at the question I know that the mugs she bought were $4 each and she got 12 of them then sold 10 of them. But I'm lost trying to write out the quadratic equation.
I know it should look like
Thank for any help on this!
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
A retailer spent $48 to purchase a number of special mugs. Two of them were broken in the store, but by selling each of the remaining mugs for $3 above the original cost per mug, she made a total profit of $22.
Construct an equation that will allow us to solve for the number of mugs, denoted by n, that were originally purchased.
:
Price paid for each mug =
:
No. of mugs sold = (n-2)
:
Selling price = + 3
;
Revenue should = cost + profit
:
Total revenue = 48 + 22 = $70:
:
#sold * Price sold = total revenue
(n-2) * [ + 3] = 70
FOIL
48 + 3n - 96/n - 6 = 70
combine like terms
3n - 96/n + 48 - 6 - 70 = 0
3n - 96/n - 28 = 0
Multiply equation by n, forming a quadratic equation:
3n^2 - 28n - 96 = 0
Factor
(3n +8)(n-12) = 0
Positive solution
n = 12 mugs originally bought
:
Check
Cost: 48/12 = $4
Sold: 10 * 7 = $70 (cost + profit)