SOLUTION: The demand and supply equations for a certain item are given by D = –5p + 40 S = –p2 + 30p – 8 Find the equilibrium price. I get sooooooo Lost on these type of proble

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: The demand and supply equations for a certain item are given by D = –5p + 40 S = –p2 + 30p – 8 Find the equilibrium price. I get sooooooo Lost on these type of proble      Log On


   

Question 84863: The demand and supply equations for a certain item are given by
D = –5p + 40
S = –p2 + 30p – 8
Find the equilibrium price.
I get sooooooo Lost on these type of problems! Help! Thanks In advance.
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 = –p2 + 30p – 8
Find the equilibrium price.
:
Equilibrium price occurs when demand = supply
:
Which means D = S
:
Which means:
-5p + 40 = -p^2 + 30p - 8
:
Arrange all terms on the left:
+p^2 - 30p - 5p + 40 + 8 = 0
:
p^2 - 35p + 48 = 0; a not-so-friendly quadratic equation
:
Requires the quadratic formula to solve: a=1; b=-35; c=48
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%281033+%29%29%2F%282%29+
p+=+%28%2B35+%2B+32.14%29%2F%282%29+
p+=+67.14%2F2
p = 33.57, 1st solution
and
p+=+%28%2B35+-+32.14%29%2F%282%29+
p+=+2.86%2F2
p = 1.43; 2nd solution
:
The 1st solution does not make sense, substitute in the demand equation,
-5(33.57) + 40 gives a negative value