Puzzle #171: Letters

The postie got to his last street. There are four houses on it.

At the first house, he delivered one-half less three of the letters he had. At the second house, he delivered two-thirds less one of the letters he then had. At the third house, he delivered three-quarters less two of the letters he then had. At the last house, he delivered the remaining three letters. [Fractions indicate of the letters the postie had. e.g. “one-half” means one-half of the letters.]

How many letters did he have when he started the street, and how many did he deliver to each house?

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, September 14, 2016 at noon Pacific Time. I will post the answer shortly after.