Question

Mike repairs televisions. His revenue, in dollars, can be modeled by the equation y = 25 + 30x, where x is the number of hours spent repairing televisions. His overhead cost, in dollars, can be modeled by the equation y=5x^2−10 , where x is the number of hours spent repairing televisions.

After how many hours does he break even?

Note: The phrase break even refers to the value where the two functions are equivalent.

Enter your answer in the box.

Answer 1

`\bf \begin{cases} y=25+30x\impliedby revenue\\\\ y=5x^2-10\impliedby cost \end{cases} \\\\\\ revenue=cost\impliedby \textit{break-even point, neither profit or loss}\qquad thus \\\\\\ 25+30x=5x^2-10\impliedby \textit{solve for`

Answer 2

h = 7

Explanation:

`25 + 30x = 5x^2 - 10\\= 5x^2-30x-35\\= 5(x^2-6x-7)\\= 5((x+1)(x-7))\\\\so...\\x = -1\\x = 7`

And we want the positive one.