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Question 1065880: In the pair of supply and demand equations below, x represents the quantity demanded in units of a thousand and p the unit price in dollars, find the equilibrium quantity and the equilibrium price.
p = 108 − 4x^2 and p = x^2 + 10x + 33
equilibrium quantity ??? Thousand units
equilibrium price ??? Dollars
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In the pair of supply and demand equations below, x represents the quantity demanded in units of a thousand and p the unit price in dollars, find the equilibrium quantity and the equilibrium price.
p = 108 − 4x^2 and p = x^2 + 10x + 33
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Use substitution to solve::
108-4x^2 = x^2 + 10x + 33
5x^2 + 10x -75 = 0
x^2 + 2x - 15 = 0
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(x-5)(x+3) = 0
Positive solution::
x = 5
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equilibrium quantity ??? 5 Thousand units
equilibrium price ??? 108-4*5^2 = 108-100 = $8 Dollars
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Cheers,
Stan H.
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