Sam’s car was fined when he gave Joe and Peter a ride, so they decided to help Sam pay the fine. Joe paid $7 more than 1/4 of the fine and Peter paid $7 less than 1/3 of the fine, leaving pay $12 less than 1/2 the fine to complete the payment. What fraction of the fine did Sam pay?
Answers:  A) $ 65  B) $ 55  C) $ 50  D) $ 60  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 + 7 ] + [ ( 1 / 3 ) f – 7 ] + [ ( 1 / 2 ) f – 12 ] f = ( 1 / 4 ) f + ( 1 / 3 ) f + ( 1 / 2 ) f – 12 multiply all terms by 12 to clear the fractions . 12 f = 3 f + 4 f + 6 f – 144 12 f = 13 f – 144 – f = – 144 f = 144 well , if the fine cost $ 144 , then sam paid the part not covered by joe or peter . half the fine is $ 72 , and sam paid $ 12 less than this : $ 60 . answer = d
Answer: D