Skylar repairs microwaves. Her revenue equals R (h) = 80 + 30h dollars for every h hours she spends repairing microwaves. Her overhead cost equals C (h) = 10h^2 - 20 dollars.

After how many hours does she break even?

Given:

R (h) = 80 + 30h

C (h) = 10h² - 20

Break even is when the revenue and overhead cost is equal and profit is 0.

R (h) - C (h) = 0

80 + 30h - (10h² - 20) = 0

80 + 30h - 10h² + 20 = 0

-10h² + 30h + 100 = 0

-10 (h² - 3h - 10) = 0

h² - 3h - 10) = 0

(h - 5) (h + 2) = 0

h (h+2) - 5 (h+2) ⇒ h² + 2h - 5h - 10 = h² - 3h - 10

h - 5 = 0; h = 5

h + 2 = 0; h = - 2

She breaks even at 5 hours. There is no negative hours so 5 is the correct answer.

R (h) = C (h)

80 + 30h = 10h² - 20

80 + 30 (5) = 10 (5²) - 20

80 + 150 = 10 (25) - 20

230 = 250 - 20

230 = 230