2002 AMC 8 Problems/Problem 25
Contents
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
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 (easiest)
Assume Moe, Loki, and Nick each give Ott . Therefore, Moe has
, Loki has
, and Nick has
. After everyone gives Ott some fraction of their money, the total money at the end situation will be the same as the original; which is
. Ott gets
. Thus, the answer is
.
~sakshamsethi
Video Solution
https://youtu.be/ysNxyATCxzg - Happytwin
https://www.youtube.com/watch?v=F-ZvPoJdnfk
Video Solution by OmegaLearn
https://youtu.be/HISL2-N5NVg?t=1267
~ pi_is_3.14
Video Solution
https://youtu.be/neLz3VW2FYQ Soo, DRMS, NM
See Also
2002 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 24 |
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