Problem:
Loki, Moe, Nick and Ott are good friends. Ott had no money, but the others did. Moe gave Ott one-fifth of his money, Loki gave Ott one-fourth of his money and Nick gave Ott one-third of his money. Each gave Ott the same amount of money. What fractional part of the group's money does Ott now have?
Answer Choices:
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Solution:
Only the fraction of each friend's money is important, so we can assume any convenient amount is given to Ott. Suppose that each friend gave Ott . If this is so, then Moe had orignally and now has , Loki had and now has , and Nick had , and now has . The four friends now have , so Ott has of the group's money. This same reasoning applies to any amount of money.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions