How many sit normally sit on the left and how many normally sit on the right?

Question

When Mrs. Bodin has a staff meeting the teachers always sit in the same seats, wither on the left side of the room or on the right side of the room. None of the teachers ever misses one of Mrs. Bodin's scintillating staff meetings.

One afternoon, just to be contrary, Mrs. Rogers sat on the right side of the room, instead of the left, where she had always sat. For the first time there were the same number of teachers on the left side of the room as on the right side of the room.

At the very next meeting, Mrs. Rogers realized the error of her ways and returned to the left side of the room. Unfortunately, Mrs. Rogers had set a bad example, and now Mrs. Ridge moved. She went from the right side of the room to the left side. Now Mrs. Bodin counted twice as many teachers on the left side of the room as on the right side.

How many teachers normally sit on the left side, and how many normally sit on the right?

Answer 1

Let L and R denote the number of teachers on the left and right respectively. We are given the following facts:

L - 1 = R + 1

L + 1 = 2 (R - 1).

From these, it should be possible to solve for L and R.