Question

Pleeaaaseee help!! I will give Brainliest!
Quick Fix Inc. repairs bikes. Their revenue, in dollars, can be modeled by the equation y=400+220x, where x is the number of hours spent repairing bikes. Their overhead cost, in dollars, can be modeled by the equation y=20x^2+160, where x is the number of hours spent repairing bikes.
After how many hours does the company break even?

Answer 1

$400+220x=20x^2+160. \newline 400+220x-20x^2-160=0. \newline 240+220x-20x^2=0. \newline -12-11x+x^2=0. \newline x^2-11x-12=0. \newline x^2+x-12x-12=0. \newline x(x+1)-12(x+1)=0. \newline (x+1)(x-12)=0 \Rightarrow x_1=-1, x_2 = 12.$

Because hours can't be negative $\Rightarrow$ the answer is 12 hours.