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. What does that mean and can you help me? Thank you!

Question 109996: The demand and supply equations for a certain item are given by
D= -5p+40
S=-p^2+30p-8
Find the equilibrium price.
What does that mean and can you help me? Thank you!
Found 2 solutions by scott8148, stanbon:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
equilibrium means supply=demand, so -5p+40=-p^2+30p-8 ... p^2-35p+48=0

find p by using the quadratic formula
Answer by stanbon(75887) (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.
What does that mean and can you help me? Thank you!
-------------------------------------------------
Equilibrium occurs when demand equals supply.
EQUATION:
D = S
-5p+40 = -p^2+30p-8
p^2-35p+48=0
p = [35 +- sqrt(1225-4*48)]/2
p = [35 +- sqrt(1033)]/2
p = [35 +- 32.14...]/2
p = (35+32.14)/2 = 33.57 or p = (35-32.14)/2 = 1.43
---------------
Which is the correct answer?
Check p = 33.57
Using p=33.57, D and S both have negative values
-------------------
Check p = 1.43
Using p = 1.43 D and S both equal 32.85
Therefore p= $1.43 is the price that coincides with equilibrium.
====================
Cheers,
Stan H.

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