Given a math problem with context and a question and 5 answer choices, the task is to provide the correct answer choice based on the problem. You must choose one of the given answer choices by letter: a, b, c, d, or e; anything else is invalid.

Problem: sam ' s car was fined when he gave joe and peter a ride, so they decided to help sam pay the fine. joe paid $ 6 more than 1 / 4 of the fine and peter paid $ 6 less than 1 / 3 of the fine, leaving pay $ 10 less than 1 / 2 the fine to complete the payment. what fraction of the fine did sam pay ?
Options: a. $ 50, b. $ 40, c. $ 35, d. $ 44, e. $ 45
a