Question 1196129
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Margin of Profit 
The margin of profit of a company is the net income divided by the total sales. 
[1] A company's margin of profit increased by 0.02 from last year. 
[2] Last year the company sold its product at $3.00 each and had a net income of $4500. 
[3] This year it increased the price of its product by $0.50 each, sold 2000 more, 
and had a net income of $7140. 
[4] The company never has had a margin of profit greater than 0.15. 
How many of its product were sold last year and how many were sold this year?
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            I numbered the sentences for easy referring.



<pre>
Let x be the number of their product that were sold last year.


From [2], we have  this expression for margin profit last year 

    {{{4500/(3x)}}},  or  {{{1500/x}}}.            (1)


From [3], we have  this expression for margin profit this year 

    {{{7140/(3.50*(x+2000))}}},  or  {{{2040/(x+2000)}}}    (2)


From [1], quantity (2) is 0.02 greater than quantity (1).  It gives this equation

    {{{2040/(x+2000)}}} - {{{1500/x}}} = 0.02.


    +-------------------------------------------------------------------+
    |    In this problem, the MAJOR STEP is to get a setup equation,    |
    |            and we successfully overcome it (!)                    |
    +-------------------------------------------------------------------+

           +---------------------------------------+
           |   To solve it is just a brute force.  |
           +---------------------------------------+



Multiply both sides by x*(x+2000)

    2040x - 1500(x + 2000) = 0.02x*(x+2000)


Simplify step by step

    2040x - 1500x - 3000000 = 0.02x^2 + 40x

    x^2 + 500x - 3000000 = 0

    (x-1500)*(x+2000) = 0


So, the rots are 1500 and -2000.  We reject the negative root,

and accept the positive one  x= 1500.


Thus last year the company sold 1500 units of the product.

This year they sold 2000 units more, i.e.  1500 + 2000 = 3500 units of the product.
</pre>

Solved.


I'd say it is a good problem of a university Olympiad level for students of  Finance department (without any joke).



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Thanks to tutor @math_tutor2020 for correcting me !