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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.

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 overhe class=

Respuesta :

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

[tex]80+24x=x^2-100[/tex]

Let's solve the equation:

[tex]\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}[/tex]

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.

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