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!
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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

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Which is the correct answer?
Check p = 33.57
Using p=33.57, D and S both have negative values
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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.
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Cheers,
Stan H.