Question

Jimmy owns a small engine repair business. The revenue, in dollars, can be modeled by the equation y = 420 + 72x, where x is the number of hours spent repairing small engines. The overhead cost, in dollars, can be modeled by the equation y = 24x² + 180 where x is the number of hours spent repairing bikes.

After about how many hours does the company break even?

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


1 h

5 h

2 h

10 h

Answer 1

y₁ = 420 + 72x
y₂ = 24x² + 180

y₁ = y₂
∴ 420 + 72x = 24x² +180
∴ 24x² - 72x - 240 = 0
∴ x² - 3x -10 = 0
∴ ( x + 2)( x - 5 ) = 0
∴ x = -2 (Unacceptable) OR x = 5

∴ The correct answer is the second ⇒⇒⇒⇒⇒ 5h