I rented a car a couple of weeks ago. I had to pay so much per day. It seems like it used to be that you had some kind of flat payment you had to pay as well. If that was the case, it doesn't seem to be any more.
Let's pretend it is the case, though. Otherwise, this example is not going to be all that great.
Car #1 - It rents for $50 a day with a flat payment of $70.
Car #2 - It rents for $42 a day with a flat payment of $120.
What is the better deal? The obvious answer is, "It depends". So we can do a little math to find out what he depends on. Two helpful equations will be:
y = 50x+70
y = 42x+120
There are many ways to solve this. Probably the easiest is the substitution method.
50x+70 = 42x+120
8x+70 = 120
8x = 50
x = 6.25 days
Students can discuss the concept of a break-even point. This situation doesn't actually have one as I doubt if any car rental company would keep track of quarter-days. When I was in school there was so much I didn't know. So this would be a good exercise in not just math, but how car rentals work and what thy might cost.
The graphing method would take a bit more work, but students would get a better idea of what was going on.
Pictured below is the darling I rented.
