Question

A student society at a large university campus decides to create a pool of bicycles that can be used by the members of the society. Bicycles can be borrowed or returned at the residence, the library, or the athletic center. The first day, 200 marked bicycles are left at each location. At the end of the day, at the residence, there are 160 bicycles that started at the residence, 40 that started at the library, and 60 that started at the athletic center. At the library, there are 20 that started at the residence, 140 that started at the library, and 40 that started at the athletic center. At the athletic center, there are 20 that started at the residence, 20 that started at the library, and 100 that started at the athletic center. If this pattern is repeated every day, what is the steady-state distribution of bicycles?

The solution is supposed to be 54% of bicycles left at residence, 29% at the library and 17% at athletic center.

Answer 1