SOLUTION: I have several of these problems - and I forget how to arrange them it has been so long. I am taking a course which involves some algebra. If I can see one in a finished state

SOLUTION: I have several of these problems - and I forget how to arrange them it has been so long. I am taking a course which involves some algebra. If I can see one in a finished state - I

Question 135015: I have several of these problems - and I forget how to arrange them it has been so long. I am taking a course which involves some algebra. If I can see one in a finished state - I should be able to do the rest: This is what I have done so far: a. Price = 48/n, b. selling price of remaining mugs = 70/n-2 and c. Mugs available for sale = n-2. - Any help is greatly appreciated. Here is the entire problem it is on a printed handout - not a text:
PROBLEM:
A retailer spent $48 to purchase a number of special mugs. Two of them were broke 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 original purchased.

a. If the price for the mugs is $48,how can we express the cost per mug?
b. 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 the information, and your answer to step a, how can we express the selling price per mug?
c. Since two of the mugs were broken in the store, how can we represent that were available for sale?
d. Use your answer from step b and c to construct an expression for the amount of money made on the sale of the remaining mugs.
e. 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 equation that states the relationship between the money made, the cost and the profit.

Level 2
Rewrite the equation that you wrote in step e on the standard form of a quadratic equation:
Ax(squared)+bx+c=0

Level 3
Solve your quadratic equation from level 2 using the quadratic formula, and answer the following questions.
a. How many mugs were purchased?
b. What was the original cost per mug?
c. What was the profit on each mug?
d. When solving a quadratic equation, there are normally two solutions. Why were you able to discard one of the solutions in this case?
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
a. GOOD WORK

b. yes, but where is the answer from a? __ try (48/n)+3

c. right again

d. mugs times selling price __ (n-2)((48/n)+3) __ FOILing __ 48+3n-(96/n)-6 __ 42+3n-(96/n)

e. p=mm-c __ 22=42+3n-(96/n)-48 __ 28=3n-(96/n)

L2. subtracting 28 and multiplying by n __ 0=3n^2-28n-96

L3
a. n=[28 +- sqrt((-28)^2-4*3*(-96)]/(2*3) __ n=[28 +- sqrt(784+1152)]/6
__ n=(28 +- 44)/6 __ n=12 and n=-8/3

b. 48/12=4

c. 22/10=2.20

d. a negative number of mugs is not realistic
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