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?	Answers.
A) $ 50	B) $ 40	C) $ 35	D) $ 44	E) $ 45

Rationale: "call the fine f . joe paid ( 1 / 4 ) f + 4 and peter paid ( 1 / 3 ) f – 4 , leaving ( 1 / 2 ) f – 5 left . if we add those three up , they should add up to f . f = [ ( 1 / 4 ) f + 6 ] + [ ( 1 / 3 ) f – 6 ] + [ ( 1 / 2 ) f – 10 ] f = ( 1 / 4 ) f + ( 1 / 3 ) f + ( 1 / 2 ) f – 10 multiply all terms by 12 to clear the fractions . 12 f = 3 f + 4 f + 6 f – 120 12 f = 13 f – 120 – f = – 120 f = 120 well , if the fine cost $ 120 , then sam paid the part not covered by joe or peter . half the fine is $ 60 , and sam paid $ 10 less than this : $ 50 . answer = a"
Answer: A