SOLUTION: the demand and supply equations for a certain item are given by d=-5p+40 S=-p^2+30p-8 Find the equillibrium price A)1.43 B)1.57 C)1.71 D)1.29

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: the demand and supply equations for a certain item are given by d=-5p+40 S=-p^2+30p-8 Find the equillibrium price A)1.43 B)1.57 C)1.71 D)1.29      Log On


   

Question 89956: the demand and supply equations for a certain item are given by
d=-5p+40
S=-p^2+30p-8
Find the equillibrium price
A)1.43
B)1.57
C)1.71
D)1.29
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The demand and supply equations for a certain item are given by
d = -5p + 40
S = -p^2 + 30p - 8
Find the equilibrium price:
:
Equilibrium price occurs when demand = Supply:
d = s
:
-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
:
Use the quadratic formula to find p: a=1; b=-35; c=48
p+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
:
p+=+%28-%28-35%29+%2B-+sqrt%28+-35%5E2+-+4+%2A+1+%2A+48+%29%29%2F%282%2A1%29+
:
p+=+%28%2B35+%2B-+sqrt%281225+-+192+%29%29%2F%282%29+
:
p+=+%28%2B35+%2B-+sqrt%281033%29%29%2F%282%29+
:
I'll let you do the math and find the value of p: