SOLUTION: A retailer bought a number of special mugs for $48. Two of the mugs were broken in the store, but by selling each of the other mugs for $3 above the original cost per mug, she mad
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Question 206420: A retailer bought a number of special mugs for $48. Two of the mugs were broken in the store, but by selling each of the other mugs for $3 above the original cost per mug, she made a total profit of $22. How many mugs did she buy and at what price per mug did she sell them? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A retailer bought a number of special mugs for $48.
Two of the mugs were broken in the store, but by selling each of the other
mugs for $3 above the original cost per mug, she made a total profit of $22.
How many mugs did she buy and at what price per mug did she sell them?
:
Let n = no. of mugs she bought
:
Price paid for each mug =
:
No. of mugs sold = (n-2); two were broken
:
Selling price = + 3; "$3 above the original cost per mug,"
;
Total revenue = 48 + 22 = $70: cost + given total profit
:
#sold * Price sold = total revenue
(n-2) * [ + 3] = 70
FOIL
48 + 3n - 96/n - 6 = 70
:
3n - 96/n + 42 = 70
:
3n - 96/n + 42 - 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
:
Find the price:
No. sold = 10 mugs; revenue = $70 = $7 for each mug
;
:
Check solution = $4 cost
cost + given profit
4 + 3 = $7
