<PRE><B>Question 206420</B>
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 = {{{48/n}}}
:
No. of mugs sold = (n-2); two were broken
:
Selling price = {{{48/n}}} + 3; &quot;$3 above the original cost per mug,&quot;
;
Total revenue = 48 + 22 = $70: cost + given total profit
:
#sold * Price sold = total revenue
(n-2) * [{{{48/n}}} + 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
{{{70/10}}} = $7 for each mug
;
:
Check solution
{{{48/12}}} = $4 cost 
cost + given profit
4 + 3 = $7</PRE>