SOLUTION: The Total cost price of certain number of identical articles is 4800..By selling the articles at 100 each,a profit equal to the cost price of 15 articles is made.Find the number of

Question 631079: The Total cost price of certain number of identical articles is 4800..By selling the articles at 100 each,a profit equal to the cost price of 15 articles is made.Find the number of articles bought
My solun
Let the articles bought be x
Then C.P of each article is 4800/x
The Selling price of x articles is 100x
The cost price of 15 items is 4800/15 = 320
So 100 x-4800/x = 320
100x^2 - 4800 = 320x
100x^2 - 320x - 4800 = 0;
10x^2-32x-480 = 0;
I am not able to find the solution.What is it I am doing wrong?? Please help me..Thanks in advance
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
I agree with the beginning of your work:
Let the articles bought be x
Then C.P of each article is 4800/x
The Selling price of x articles is 100x.

The mistake is in the next step.
Buying x articles the merchant paid 4800/x for each one.
That does not mean that the merchant would pay 4800/15=320 for each one of only 15 of those articles.
It does not mean that the total cost for 15 articles is 320, either.
You cannot say x=15 for this step, when the value of x is what you are trying to find.

Instead, you should think that the cost for 15 articles (at a cost per article of 4800/x, as you found before) is .
The merchant sells all the articles for a total of 100x, which is, of course, more than the 4800 cost of all the articles.
The difference is the profit, that happens to be , so

Now let's solve, and then we can make sure that it makes sense.
--> (multiplying both sides times x).
--> (dividing both sides by 100).
--> (subtracting 720 from both sides, to get a nice quadratic equation).
We know that solving by factoring could be an option, because x should be a nice positive integer.
We need two factors that multiplied equal -720, and add up to -48.
The factors -60 and 12 work.
The quadratic polynomial can be factored as:

So -->
with solutions and .
Of course we know that x, the number of articles bought and sold, is not a negative number, so we realize that must be discarded because it does not make sense.
The merchant bought articles for a total of 4800 (dollars, or whatever the currency is).

COMMON SENSE VERIFICATION:
The cost per article was .
On selling the 60
articles at 100 each, the merchant collected
The profit was the 6000 collected minus the 4800 cost, or

The cost of 15 item was , the same amount as the total profit.
If the merchant had borrowed the original 4800 (from a relative, in a no-interest loan), the loan can now be repaid, and the merchant is left with 1200 to use to buy maybe 15 more of those articles (assuming he/she can still get the same good price from his supplier).
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