Sam’s car was fined when he gave Joe and Peter a ride, so they decided to help Sam pay the fine. Joe paid $8 more than 1/4 of the fine and Peter paid $8 less than 1/3 of the fine, leaving pay $15 less than 1/2 the fine to complete the payment. What fraction of the fine did Sam pay? Select the correct option
A) $ 70
B) $ 72
C) $ 73
D) $ 74
E) $ 75

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 + 8 ] + [ ( 1 / 3 ) f – 8 ] + [ ( 1 / 2 ) f – 15 ] f = ( 1 / 4 ) f + ( 1 / 3 ) f + ( 1 / 2 ) f – 15 multiply all terms by 12 to clear the fractions . 12 f = 3 f + 4 f + 6 f – 180 12 f = 13 f – 180 – f = – 180 f = 180 well , if the fine cost $ 180 , then sam paid the part not covered by joe or peter . half the fine is $ 90 , and sam paid $ 15 less than this : $ 75 answer = e"
Answer: E