Question 1201604
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A shopkeeper bought x chairs for a total cost of $650. 
He sold them at $4 each more than they had cost him. 
Six chairs were damaged and could not be sold . 
If he made a profit of $98 on the whole transaction, form and solve an equation in x.
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The price he bought them was  {{{650/x}}}  dollars per chair.


He made a profit of $98 on the whole transaction - hence, he sold (x-6) chairs for 650+98 = 748 dollars.


Thus the price he sold the chairs was  {{{748/(x-6)}}}  dollars per chair.


The difference between the selling price and buying price was $4 (given) - so we write this equation

    {{{748/(x-6)}}} - {{{650/x}}} = 4  dollars.


    +---------------------------------------------+
    |   At this point, the setup is complete.     |
    |   Now your task is to solve this equation.  |
    +---------------------------------------------+


For it, multiply both sides by x*(x-6).  You will get

    748x - 650(x-6) = 4x*(x-6).


Simplify

    748x - 650x + 650*6 = 4x^2 - 24x

    98x + 3900 = 4x^2 - 24x

    4x^2 - 24x - 98x - 3900 = 0

    4x^2 - 122x - 3900 = 0

    2x^2 - 61x - 1950 = 0.


Apply the quadratic formula.

You will get two roots: one positive and one negative.


The positive root is 50.


Discard the negative root and accept the positive one.


<U>ANSWER</U>.  x = 50 chairs were bought.
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Solved.