A clothing store determines that in order to sell x shirts, the price per shirt should be p (x) = 100-x dollars. Getting x shirts from the supplier costs the store C (x) = 1,600+20x dollars. If the store's revenue from selling x shirts is R (x) = x⋅p (x), for what value of x will the store's cost and revenue be equal?

x = - 40

Step-by-step explanation:

Cost

C (x) = 1,600+20x

P (x) = 100-x

Revenue=x*p (x)

=x * (100-x)

=100x-x^2

Cost=Revenue

1600+20x=100x-x^2

1600+20x-100x+x^2=0

1600-80x+x^2=0

Solve using quadratic formula

Formula where

a = 1, b = 80, and c = 1600

x=-b±√b2-4ac/2a

x=-80±√80^2-4 (1) (1600) / 2 (1)

x=-80±√6400-6400 / 2

x=-80±√0 / 2

The discriminant b^2-4ac=0

so, there is one real root.

x = - 80/2

x = - 40