20 Jan '06 15:211 edit

Suppose that I own a car rental company with 3 offices. One office is in Denver, one is in Boulder, and one is in Pueblo (All in Colorado, USA). My office is successful enough that I rent out all of the cars in all of the offices every day. Also, assume that every car that is rented is also returned on the same day. Now, my customers' behavior is exactly the same from one day to the next. So, I know for a fact that 50% of the cars rented in the Denver site will be returned to the Denver site. 30% of the cars rented in Denver are returned to Boulder, and the last 20% of the cars rented in Denver are returned to Pueblo. 40% of the cars rented in Boulder are returned to Denver, and the other 60% are returned to Boulder. 40% of the cars rented in Pueblo are returned to Denver, 10% returned to Boulder, and 50% returned to back to Pueblo. If I have X cars to rent, how many cars should I originally have in each site so that at the end of the day, each site will have the same number of cars it started the day with? For those who'd like a hint, request it via PM.