Kim is painting the outside of her house, Joe will charge her $250 plus $14/hr. Bill will charge her $22/hr. How many hours the job should take for Joe's estimate be the cheapest?

Step-by-step explanation:

This is an inequality problem. If we want Joe's service to be cheaper, then the inequality is set up like this:

14x + 250 < 22x

where x is the number of hours.

Solving we get

250 < 8x so

31.25 < x or equivalently,

x > 31.25

That means that all hours less than 31.25 would put Bill's as the cheaper service. All hours greater than 31.25 would put Joe's as the cheaper service.