Question

Skylar repairs washing machines. Her revenue, in dollars, can be modeled by theequationy = 80+ 24x, where x is the number of hours spent repairingmicrowaves. Her overhead cost, in dollars, can be modeled by the equationy=x2 – 100, where x is the number of hours spent repairing washingmachines.After how many hours does she break even?Note: The phrase break even refers to the value where the two functions areequivalent.

Answer 1

The company breaks even when the revenue and cost are equal, then we have to solve the equation:

$80+24x=x^2-100$

Let's solve the equation:

$\begin{gathered} 80+24x=x^2-100 \\ x^2-24x-100-80=0 \\ x^2-24x-180=0 \\ (x-30)(x+6)=0 \\ then \\ x=30 \\ or \\ x=-6 \end{gathered}$

Since we can't have a negative number of hours we conclude that the company will break even when x=30, that is after 30 hours.