School Help - Infinity

[EternalWrath]

OK, I have a math quiz Monday, and there is going to be a bonus problem about the concept of infinity. It goes something like this:

There exists a town that has an infinite number of hotels, and each hotel has an infinite number of rooms. One day, a group of cannibals (yes, my math teacher is very odd ) destroy all of the hotels and set up their own, which has an infinite number of rooms as well. The first question is: Is it possible to put all the people who lost their hotel room into this new hotel? If so, how would you organize everybody to fit in it?

To explain in concrete terms, say we had 2 hotels of infinite rooms. We would organize these people into the new hotel by having everyone from Hotel #1 go into an odd room while everyone from Hotel #2 goes to an even room. Hence, we have a procedure to fit everyone inside. In equation terms, the room number for someone from Hotel #1 is 2x-1 and for Hotel #2 2x. If there were 3 hotels involved, the equations would be 3x-2, 3x-1, and 3x, and so on.

So how would I explain this procedure in terms of infinite hotels? I thought of using summations or modulo, but both of these are concepts we have not covered in class yet, and our math teacher told us that it does not require advanced math, but rather logically reasoning. Thanks for your help.