SOLUTION: D=-200p + 35,000The supply equation is predicted to be S= -p^2 +400p –20,000Find the equilibrium price.

Algebra ->  Equations -> SOLUTION: D=-200p + 35,000The supply equation is predicted to be S= -p^2 +400p –20,000Find the equilibrium price.      Log On


   

Question 122059: D=-200p + 35,000The supply equation is predicted to be
S= -p^2 +400p –20,000Find the equilibrium price.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
D =-200p + 35,000 The supply equation is predicted to be
S = -p^2 +400p –20,000 Find the equilibrium price.
:
I assume you mean that equilibrium price (p) occurs when D = S, so we have;
:
-200p + 35000 = -p^2 + 400p - 20000
:
Arrange as a quadratic equation on the left:
+p^2 - 200p - 400p + 35000 + 20000 = 0
:
p^2 - 600p + 55000 = 0
:
Use the quadratic formula to find p:
a = 1; b = -600; c = 55000
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
:
p+=+%28-%28-600%29+%2B-+sqrt%28-600%5E2+-+4+%2A+1+%2A+55000+%29%29%2F%282%2A1%29+
:
p+=+%28600+%2B-+sqrt%28360000+-+220000+%29%29%2F%282%29+
:
p+=+%28600+%2B-+sqrt%28140000%29%29%2F%282%29+
:
p+=+%28600+%2B-+374.166%29%2F%282%29+; found the square root of 140000
Solution 1
p+=+%28600+%2B+374.166%29%2F%282%29+;
p+=+%28974.166%29%2F%282%29+;
p = $487.08
:
Solution 2:
p+=+%28600+-+374.166%29%2F%282%29+;
p+=+%28225.834%29%2F%282%29+;
p = $112.92
:
You should check both solutions by substitution in the original equation