How old is Zeke, who is sitting in chair #5?

Question

Nine people sitting in a circle notice a remarkable thing: each person’s age is the average of the ages of the people sitting directly next to him or her. Betty, sitting in chair #1, is 15 years old. How old is Zeke, who is sitting in chair #5?

Answer 1

My seat of the pants GUESS:

 

To have the rule apply all the way around the circle, they all have to be the same age.