find the equilibrium quantity and the equilibrium price. p = 87 − 3x2 and p = x2 + 8x + 27

Question

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

Answer 1

By setting both equations equal to each other:

p = 87 - 3x^2 = x^2 + 8x + 27

Push all terms to one side of the equation:

0 = 4x^2 + 8x - 60

Divide by 4:

0 = x^2 + 2x - 15

Factor terms:

0 = (x+5)*(x-3)

x = -5, 3

Taking the positive solution, x = 3

p = 87 - 3x^2 = 87 - 3*(3)^2 = 87 - 27 = p = 60