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? Choose the most appropriate option:
A) $50
B) $40
C) $35
D) $44
E) $45
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.   12F = 3F + 4F + 6F – 120   12F = 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.   $50nswer = $50
<result>A</result>
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?