The Salesman and the Eggs

An egg salesman was asked how many eggs he had sold that day. He replied, “My first customer said, ‘I’ll buy half your eggs and half an egg more.’ My second and third customers said the same thing. When I had filled all three orders I was sold out and I did not have to break a single egg all day.” How many eggs had he sold in all?

(Source: Solve It!, Fixx, J., 1978.)

What if the customers bought one-third of the eggs and one-third an egg more? How many eggs would be sold in all?