SOLUTION: It's a story where you are supposed to pull out information to build and a quadratic equation step-by-step, and then possible solve it. Here's the story; "A retailer spent $48 to

Question 118188This question is from textbook Strategies for problem solving workbook
: It's a story where you are supposed to pull out information to build and a quadratic equation step-by-step, and then possible solve it. Here's the story;
"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."
Step 1) If the price for n mugs is $48, how can we express the cost per mug?
I figured it out to be: 48/n=y
Step 2) we are told that the retailer, in order to make a specific profit, sells the remaining mugs for $3 more than the original cost per mug. using this information, and your answer to step 1, how can we express the selling price per mug?
I figured it out as: n(y+3)=70, this is from cost $48 for all mugs plus the profit of $22.
Step 3) Since two of the mugs were broken in the store, how can we represent the number of mugs available for sale?
I figured it be: n-2
Step 4) Using your answers from step (2) and (3)construct an expression for the the amount of money made on the sale of the remaining mugs.
I figured that out to be: n-2+n(y+3)=70
Step 5) The profit on the mugs can be found by subtracting the cost of the mugs from the amount of money made on the sale of the mugs. Write an eqution that states this relationship between the money made, the cost, and the profit.
I know the equation has to equal -48+70=22, but how...
is it like: -48+(n-2)+n(y+3)=22
Then to top this off rewrite the equation that you wrote in step (5) in the standard form of a quadratic equation.
Please tell me if I'm on the right track, or at least help get to the track? This question is from textbook Strategies for problem solving workbook

Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
1) an expression, not an equation ___ 48/n is correct

2) 3 more than the original cost per mug is 1) plus 3 ___ (48/n)+3 or (48+3n)/n

3) n-2 is correct

4) again, an expression ___ number of mugs times cost per mug ___ (n-2)((48+3n)/n)

5) now, an equation ___ 22=(n-2)((48+3n)/n)-48

22n=(n-2)(48+3n)-48n ___ 70n=48n+3n^2-96-6n ___ 3n^2-28n-96=0 ___ (3n+8)(n-12)=0
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