Quadratic Equations

rcwitt · 2011-01-20 11:14:49

This class is getting ridiculous. We have managed to go from large prime numbers to permutations & combinations to logical reasoning (where I had to explain the error in Zeno's "Achilles and the Tortoise" Paradox) to quadratic equations. I am stumped yet again. I am quickly realizing that the accelerated classes are incredibly challenging when your instructor expects you to research on your own to learn the material on your own.
Anyway, below is the problem I have now. It consists of several parts. I will put what I have come up with as answers, but the later questions don't work with my answers. It's hard to explain, but, hopefully it'll become clear.

Problem:

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.

(a) If the price for n mugs is $48, how can we express the cost per mug?

***** My answer is below*****

(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 this information, and your answer to step (a), how can we express the selling price per mug?

*****My answer is below*****

(c) Since two of the mugs were broken in the store, how can we represent the number of mugs available for sale?

*****My answer is below*****

(d) Use your answers from steps (b) and (c) to construct an expression for the amount of money made on the sale of the remailing mugs.

*****My answer is below*****

*****I think I have it right so far*****

(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 this relationship between the money made, the cost, and the profit. HINT: If written correctly, your equation will contain only one variable, n.

*****My answer would be below, if I could figure one out to put there.*****

Then, the following problem refers to the answer that I don't have. It is:

Rewrite the equation that you wrote in step (e) in the standard form of a quadratic equation:

My head feels like it is going to explode!! I know I have been asking for a lot of help lately, and you have no idea how much I appreciate your assistance. I really have learned more here than I have in class. If it gets to where I am wearing out my welcome, please let me know. I really don't want to have to ask for help all of the time, but I don't know where else to go. I am going to continue to try to figure it out while waiting. I have actually discovered some errors in my equations while typing them out (the corrected versions are in this post), so hopefully, I can figure it out. If I do manage to do so, I will post a follow up message.

Charlie

bobbym · 2011-01-20 11:24:49

Hi Charlie;

That is the purpose of the forum, to have people post questions. You cannot wear out your welcome or my patience.

If you get an answer of 12 mugs at 4 bucks apiece you are okay.

Onyx · 2011-01-20 11:28:36

Shouldnt the answer to d just be a*p?

bobbym · 2011-01-20 11:41:58

I get for a quadratic:

n = 12 as the number of original mugs sold at 4 bucks apiece.

rcwitt · 2011-01-20 11:50:13

Bobby,
You got ahead of me, I am still trying to figure out how to properly express (e). LOL!

Charlie

bobbym · 2011-01-20 11:53:28

What I did was to point you towards the answer. That way you can back engineer the rest. If not then we will have to rewrite the whole approach. It is a little advanced but since they are racing you through 1100 years of math in 3 hours it seems appropriate. Play with it a little bit and see if you can work it out by yourself first.

Math Is Fun Forum

#1 2011-01-20 11:14:49

Quadratic Equations

#2 2011-01-20 11:24:49

Re: Quadratic Equations

#3 2011-01-20 11:28:36

Re: Quadratic Equations

#4 2011-01-20 11:41:58

Re: Quadratic Equations

#5 2011-01-20 11:50:13

Re: Quadratic Equations

#6 2011-01-20 11:53:28

Re: Quadratic Equations

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