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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 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 dollars per chair.
The difference between the selling price and buying price was $4 (given) - so we write this equation
- = 4 dollars.
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| At this point, the setup is complete. |
| Now your task is to solve this equation. |
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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.