SOLUTION: Please help with this word problem. The demand equation for a certain type of printer is given by D = -200p + 35000 The supply equation is predicted to be S = -p^2 + 400p - 2

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Question 42476: Please help with this word problem.
The demand equation for a certain type of printer is given by
D = -200p + 35000
The supply equation is predicted to be
S = -p^2 + 400p - 20000
Find the equilibrium price.
Thanks!!
Answer by Nate(3500) 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 + 35000 or y = -200p + 35000
The supply equation is predicted to be
S = -p^2 + 400p - 20000 or y = -p^2 + 400p - 20000
So ....
y = -p^2 + 400p - 20000
-200p + 35000 = -p^2 + 400p - 20000
0 = -p^2 + 600p - 55000
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ap%5E2%2Bbp%2Bc=0 (in our case -1p%5E2%2B600p%2B-55000+=+0) has the following solutons:

p%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28600%29%5E2-4%2A-1%2A-55000=140000.

Discriminant d=140000 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-600%2B-sqrt%28+140000+%29%29%2F2%5Ca.

p%5B1%5D+=+%28-%28600%29%2Bsqrt%28+140000+%29%29%2F2%5C-1+=+112.917130661303
p%5B2%5D+=+%28-%28600%29-sqrt%28+140000+%29%29%2F2%5C-1+=+487.082869338697

Quadratic expression -1p%5E2%2B600p%2B-55000 can be factored:
-1p%5E2%2B600p%2B-55000+=+-1%28p-112.917130661303%29%2A%28p-487.082869338697%29
Again, the answer is: 112.917130661303, 487.082869338697. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B600%2Ax%2B-55000+%29

+graph%28+1000%2C+1000%2C+100%2C+500%2C+-10%2C+10%2C+-x%5E2+%2B+600x+-+55000%29+