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.

Answer 1

I added a screenshot with the complete question.

Answer:
5 hours

Step-by-step explanation:
We are given that:
Revenue equation:
y = 420 + 72x
Overhead equation:
24x² + 180

We are asked to get the break-even point which is calculated by equating the revenue to the overhead cost.

This can be done as follows:
revenue = overhead cost
420 + 72x = 24x² + 180
24x² + 180 - 420 - 72x = 0
24x² - 72x -240 = 0
(x-5)(x+2) = 0

either: x-5=0 ..........> x = 5 hours (accepted value)
or: x+2=0 .......> x = -2 hours (rejected value as time cannot be negative)

Based on the above:
break-even occurs at 5 hours

Hope this helps :)