Question 1172719
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The costs $C of making a school bag is partly constant and partly varies inversely as the total number N of bags made. 
When 200 bags are made, the cost per bag is $60. When 500 bags are made, the cost per bag is $45. 
How many bags are made if the cost per bag is $40? Find the cost per bag if 400 bags are made.
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The problem's formulation is TERRIBLE (!)


This language was in use at parish country schools of the before-Shakespearean times

and was totally changed and replaced starting from post-Newtonian era.


Now nobody understands this language --- the proofs are the posts of the two other English-speaking tutors.


The meaning of this post (if translate it to the contemporary English) is THIS : 



<pre>
        Consider the function C(N) = A + (B/N),  where "A" and "B" are constants, whose values are not known now.

        Given :  C(200) = 60 dollars,   C(500) = 45 dollars.

        Find  N,  if  C(N) = 40 dollars.
</pre>


OK, now I will start based on my re-formulation.


<pre>
At  N = 200,  we have this equation   

    {{{A + B/200}}} = 60  dollars     (1)



At  N = 500, we have this equation

    {{{A + B/500}}} = 45  dollars     (2)



Subtracting equation (2) from equation (1), you get

           {{{B/200}}} - {{{B/500}}} = 60-45 = 15


Multiply both sides by 1000.  You will get

           5B - 2B = 15000,

             3B    = 15000

              B    = 15000/3 = 5000.


Then from (2)

    {{{A + 5000/500}}} = 45,   or

       A + 10 = 45

       A      = 45 - 10 = 35.


To complete the solution, you need find N from the equation

     C(N) = 40,   or  {{{35 + 5000/N}}} = 40.


The last equation gives

    {{{5000/N}}} = 40-35 = 5

        N  = {{{5000/55}}} = 1000.


<U>ANSWER</U>.  N = 1000.
</pre>

Solved, answered, explained and completed.