2002 AMC 8 Problems/Problem 25
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[hide]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?
Solution 1
Since Ott gets equal amounts of money from each friend, we can say that he gets dollars from each friend. This means that Moe has dollars, Loki has dollars, and Nick has dollars. The total amount is dollars, and since Ott gets dollars total, .
Solution 2
We can assign any natural number to the price that Ott's friends gave him. For this example, we will use 5.
Moe gave Ott a fifth of his money, and also five dollars. So in total Moe has 25 dollars.
Loki gave Ott a fourth of his money, and also five dollars. So in total Loki has 20 dollars.
Nick gave Ott a third of his money, and also five dollars. So in total Nick has 15 dollars.
which is the total money the group gave Ott.
is the group's balance. Therefore, the fraction of the group's money that Ott now has is .
Video Solution
https://www.youtube.com/watch?v=F-ZvPoJdnfk ~David
See Also
2002 AMC 8 (Problems • Answer Key • Resources) | ||
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