SOLUTION: 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

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Question 1201604: 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 .
I did :
x(x-6)-650=98
x^2-6x-748=0 (can't be factored)
The answer on my book is 50 .
So, how is this solved?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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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.
~~~~~~~~~~~~~~~~~~~~~ 

The price he bought them was  650%2Fx  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%2F%28x-6%29  dollars per chair.


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

    748%2F%28x-6%29 - 650%2Fx = 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.


ANSWER.  x = 50 chairs were bought.

Solved.