SOLUTION: A retailer spent $48 to purchase a number of special mugs. Two of them were broken i the store, but by selling each of the remaining mugs for $3 above the original cost per mug, sh

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Question 33681This question is from textbook
: A retailer spent $48 to purchase a number of special mugs. Two of them were broken i 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 solve for the number of mugs, denoted by n, that were originally purchased. If the price for n mugs is $48, how can we express the cost per mug? This question is from textbook

Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
let the number of mugs be x
so cost of each mug is 48/x.
cost of mug for selling = 48/x +3.(three more)
total number of mugs sold = x-2.
total profit= 48 + 22 = 70.00
Equation:
%2848%2Fx%2B3%29+%28x-2%29+=+70
Expand:
48-96%2Fx%2B3x-6=70
Multply the whole equation by x to remove the fraction adn simplify:
48x-96+3x^2-6x=70x
3x^2-28x-96=0
Factor:
(x-12)(3x+8)
x=12