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Profit - algebraic solution

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Profit - algebraic solution

by AleksandrM » Sat Jun 14, 2008 1:16 pm
Again, I am not interested in how you would use the answer choices to your adventage. I am interested in an algebraic solution:

In the first week of last month, Company X realized an average wholesale profit of $5304 per day from the sale of q units of Product Y. Which of the following CANNOT be the difference between Product Y’s sale price and cost per unit?

A) $3
B) $4
C) $7
D) $11
E) $51

Thanks!
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by litteraround » Sat Jun 14, 2008 4:14 pm
I don't think it is possible to have a purely algebraic solution here. Because, if you could, then your answer will have to be what IS the difference. As, it is clear from the question itself that there are several choices for What IS, and only one of What IS NOT (which itself is impossible to be found algebraically). Hope you can follow my logic.
'
So, at some point, you are gonna have to use the answer choices to get to the answer.

Now, I got the answer (d) 11.

Here's how I did it....

Profit = Total Sales Price - Total Cost Price (Per day) = 5304

Therefore, total profit over a period of 7 days will be 5304*7.

Now, let the difference of sales price per unit and cost price per unit (which is essentially profitt per unit) be x.

Therefore, total 'difference' will be (if no. of units produced over a week are 'q') is 'qx', which is in effect total profit (profit per unit*total no. of units).

So, we have, 5304*7=qx

or, q = (5304*7)/x

Since, q can only be a whole number,

we have to consider the answer choice that gives a fraction when we plug it into x.

The one that is a problem is 11. so, there...
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by AleksandrM » Sat Jun 14, 2008 5:10 pm
Not bad. My appraoch was to actually write out:

qp - qc/7 = 5304 [factor out q]

q (p - c) = 5304 * 7

Then I realized that p - c is the profit per unit and can be treated as a single unit, so I just did what you did. I was wondering, though, whether there is another approach.

We'll see what the rest of the community attempts. Thanks, though. :)
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