An egg salesman was asked how many eggs he had sold that day. He replied, "My first customer said, 'I'll buy half of your eggs plus half of an eggs.' My second and third customers made the same order as customer number one. When I had filled all three orders I was sold out and I did not have to break a single egg all day."

Question

How many eggs did the egg salesman start with?

Answer 1

1st customer: x/2 + 1/2 = (x+1)/2, leaving (x-1)/2
2nd customer: (x-1)/4 + 1/2 = (x+1)/4, leaving (x-3)/4
3rd customer: (x-3)/8 + 1/2 = (x+1)/8 leaving 0
so,
(x+1)/2 + (x+1)/4 + (x+1)/8 = x
x = 7
it's easy to check that 4+2+1 = 7

Answer 2

1st = e/2 + 1/2

2nd = [(e - e/2 - 1/2) / 2] + 1/2 = e/4 + 1/4

3rd = [(e - e/2 - 1/2 - e/4 - 1/4) / 2] + 1/2 = e/8 + 1/8

e = (7e / 8) + 7/8

8e = 7e + 7