How many did he start out with?

Question

The egg vendor calls on his first customer and sells half his eggs and half an egg. To the second customer he sells half of what he had left and half an egg, and to the third customer he sells half of what he had then left and half an egg. By the way he did not break any eggs. In the end three eggs were remaining.
How many did he start out with?

Answer 1

He has started with 7 eggs.
The first person bought one half of his eggs plus one half an egg (3 1/2 + 1/2 = 4 eggs), this left him 3 eggs. The second person bought one-half of his eggs plus one half an egg, (1 1/2 + 1/2 = 2 eggs) leaving the man 1 egg.
The last person bought one-half of his eggs plus one-half an egg, (1/2 + 1/2 = 1 egg) leaving no eggs.

Comments

but in the end three eggs were remainig

Answer 2

he has started with 31 eggs
to the first person he sell 15 1/2 + 1/2 = 16 eggs than 15 eggs remaining
to the second person he sell 7 1/2 +1/2 = 8 eggs than 7 eggs remaining
to the third person he sell 3 1/2 + 1/2 = 4 eggs than 3 eggs remaining