Find the equilibrium quantity (in hundred units)? Find the equilibrium price (in dollars)

Question

The weekly demand and supply functions for Sportsman 5 ✕ 7 tents are given by

p = −0.1x² − x + 60 and

p = 0.1x² + 2x + 40

respectively, where p is measured in dollars and x is measured in units of a hundred.

Answer 1

add the two equations to get

2P = 0 + x + 100

P = x/2 + 50

subtract the 2 equations to eliminate P and then solve for x

0 = .2x^2 + 3x -20

multiply by 5

0 = x^2 + 15 -100

factor

(x+20)(x-5) = 0

set each factor equal to zero and solve for x

x =-20, 5

ignore the negative solution

x=5 = 500 tents at equilibrium price

p= x/2 +50 = 5/2 + 50 = $52.50 per tent, at equilibrium price