Respected sirs I want this question answer

Question

Market Equilibrium

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

p = −0.1x² − x + 76 and

p = 0.1x² + 2x + 56

respectively, where p is measured in dollars and x is measured in units of a hundred. Find the equilibrium quantity (in hundred units).

_________ hundred units

_________ Find the equilibrium price (in dollars).

$ 

Answer 1

set the two equations equal and solve for x or just subtract one equation from the other to eliminate p and solve for x

Either way you get .2x² + 3x -20 =0

Multiply by 5 to simplify, a little

x² + 15x -100 = 0

You can factor this, surprisingly as 100 = 20 x 5 and 20 -5 = 15 the middle term coefficient

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

x=-20, 5 ignore the -20 as x>0

x=5 is the demand and supply in equilibrium, or in units of 100, as x really is 500

Plug that into either of the original equations to get the price, p

p=.1(5)² +2(5) +56 = 1/10 (25) + 10 +56 = 2.5 + 10 + 56 = 68.5

P=$68.5 at that price supply & demand are equal at 500 tents

That's a price of $68.50 per one hundred tents, which sells 500 tents

or plug 5 into the other original equation:

-.1(5)² -5+ 76 = =-2.5 -5+76 = 68.5