SOLUTION: The demand equation for a certain type of printer is given by D=-200p+35,500. The supply equation is predicted to be S=-p^2+400p-20,000. Find the equilibrium price.

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Question 83821: The demand equation for a certain type of printer is given by D=-200p+35,500. The supply equation is predicted to be S=-p^2+400p-20,000. Find the equilibrium price.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The demand equation for a certain type of printer is given by D=-200p+35,500. The supply equation is predicted to be S=-p^2+400p-20,000. Find the equilibrium price.
:
This occurs when Demand (D) = Supply (S) so put the two equations equal to each other:
:
-200p + 35500 = -p^2 + 400p - 20000
:
p^2 - 200p - 400p + 35500 + 20000 = 0; Arrange all terms on the left
:
p^2 - 600p + 55500 = 0; our old friend the quadratic equation
:
Use the quadratic formula to find p: a=1; b=-600; c=55500
p+=+%28-%28-600%29+%2B-+sqrt%28-600%5E2+-+4+%2A+1+%2A+55500+%29%29%2F%282%2A1%29+
p+=+%28%2B600+%2B-+sqrt%28360000+-+222000+%29%29%2F%282%29+
p+=+%28%2B600+%2B-+sqrt%28138000+%29%29%2F%282%29+
p+=+%28600+%2B-+371.5%29%2F2
Two solutions:
p+=+971.5%2F2
p = $485.75
and
p+=+228.5%2F2
p = $114.25
:
:
Check solution using the $485.75 price, using a calc see if they are equal:
-200p + 35500 =
-200(485.75) + 35500 = -61650
:
-p^2 + 400p - 20000
-(485.75^2) + 400(485.75) - 20000 = -61653;
Since this produces a negative value, it's probably the lower price we want
:
Check the p= $114.25 solution the same way.
-200(114.25) + 35500 = 12650
-(114.25^2) + 400(114.25) - 20000 = 12647; close enough