2002 AMC 8 Problems/Problem 25
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 has . Using the information given in the problem, we can conclude that Loki has
and Nick has
. After everyone gives Ott some fraction of their money, he gets
. reviewing the situation, Moe now has
, Loki has
, and Nick has
. Ott has $\frac{3}{$ (Error compiling LaTeX. Unknown error_msg)4+3+2+3$}$ (Error compiling LaTeX. Unknown error_msg) fraction of the group's money. Thus, the answer is
.
~sakshamsethi
Video Solution
https://youtu.be/ysNxyATCxzg - Happytwin
See Also
2002 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 24 |
Followed by Last Problem | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.