Puzzle #56: Bacon!

Mmm, bacon!

Mom fried some bacon strips for breakfast, then took her yogurt and went out to her greenhouse. (Partly for the fun of gardening, and partly to avoid the arguments about fair and unfair shares.)

The first son up grabbed one-third of the bacon strips and took two more for good measure. The second son up grabbed one-half of the remainder, but then put one back. The third son up grabbed one-half of the remainder and then took another.

At this point, there were two pieces left which Dad got. How many pieces did Mom fry up?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, July 2, 2014> at noon Pacific Time. I will post the answer shortly after.