SOLUTION: The demand and supply equations for a certain item are given by D = �5p + 40 S = �p^2 + 30p � 8 Find the equilibrium price.

Question 104060: The demand and supply equations for a certain item are given by
D = �5p + 40
S = �p^2 + 30p � 8
Find the equilibrium price.

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
he demand and supply equations for a certain item are given by
D = �5p + 40
S = �p^2 + 30p � 8
Find the equilibrium price.
:
The equilibrium price (p) occurs when D = S, therefore:
:
-5p + 40 = -p^2 + 30p - 8
:
Arrange as a quadratic equation on the left:
+p^2 - 5p - 30p + 40 + 8 = 0
:
p^2 - 35p + 48 = 0
:
This equation requires the quadratic formula to solve: a = 1; b =-35; c= 48

Two solutions

p = 33.57
and

p = $1.43
:
Only the lower price make sense, the higher value will give negative values in the original expressions.
:
You can check this by substituting 1.43 for p
-5(1.43) + 40 = -(1.43^2) + 30p - 8
-7.15 + 40 = -2.0449 + 30(1.43) - 8
32.85 = -2.0449 + 42.9 - 8
32.85 = 32.85 equality reigns
:
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