SOLUTION: A furniture company sells 3000 chairs per week at a price of $150 apiece; when the price is lowered to $125, the company sells 3500 chairs per week. If the company wishes to liqui

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Question 120954: A furniture company sells 3000 chairs per week at a price of $150 apiece; when the price is lowered to $125, the company sells 3500 chairs per week. If the company wishes to liquidate its entire remaining inventory of 4250 chairs in the next week, what price should they seek?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A furniture company sells 3000 chairs per week at a price of $150 apiece; when the price is lowered to $125, the company sells 3500 chairs per week. If the company wishes to liquidate its entire remaining inventory of 4250 chairs in the next week, what price should they seek?
:
Let x = price of the chairs; Let y = no. of chairs sold
Find the slope of the equation m = %28y2-y1%29%2F%28x2-x1%29
x1 = 150; y1 = 3000
x2 = 125; y2 = 3500
:
m = %283500-3000%29%2F%28125-150%29 = 500%2F%28-25%29 = -20 is the slope
:
Using the point/slope equation: y - y1 = m(x - x1)
y - 3000 = -20(x - 150)
:
y - 3000 = -20x + 3000
:
y = -20x + 3000 + 3000
:
y = -20x + 6000 is our equation
:
to find the price to sell all 4250 chairs, make y = 4250 and find x
-20x + 6000 = 4250
-20x = 4250 - 6000
-20x = -1750
x = %28-1750%29%2F%28-20%29
x = +$87.50 is the price to sell 4250 chairs.
:
:
You can check this by substituting each given value for x in our equation,
and confirm that it equals the given y value