find the equilibrium quantity and the equilibrium price. p = 112 − 3x2 and p = x2 + 4x + 32

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

112-3x^2 = x^2 + 4x + 32

4x^2 + 4x - 80 = 0

x^2 + x - 20 = 0

(x+5)(x-4) = 0

x =4 (ignore the negative solution of -5)= 4,000 = equilibrium quantity demanded & supplied

p = 16 + 16 + 32 = $64

p = 112 -3(4)^2 = 112-48 = $64 = equilibrium price