# Difference between revisions of "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?

$\text{(A)}\ \frac{1}{10}\qquad\text{(B)}\ \frac{1}{4}\qquad\text{(C)}\ \frac{1}{3}\qquad\text{(D)}\ \frac{2}{5}\qquad\text{(E)}\ \frac{1}{2}$

## Solution

Since Ott gets equal amounts of money from each friend, we can say that he gets $x$ dollars from each friend. This means that Moe has $5x$ dollars, Loki has $4x$ dollars, and Nick has $3x$ dollars. The total amount is $12x$ dollars, and since Ott gets $3x$ dollars total, $\frac{3x}{12x}= \frac{3}{12} = \boxed{\text{(B)}\ \frac14}$. $\blacksquare$

## Solution 2 (easiest)

Assume Moe, Loki, and Nick each give Ott $1$. Therefore, Moe has $5$, Loki has $4$, and Nick has $3$. After everyone gives Ott some fraction of their money, he gets $1$ $+$ $1$ $+$ $1$ $=$ $3$. reviewing the situation, Moe now has $5$ $-$ $1$ $=$ $4$, Loki has $4$ $-$ $1$ $=$ $3$, and Nick has $3$ $-$ $1$ $=$ $2$. Ott has $\frac{3}{4+3+2+3}$ fraction of the group's money. Thus, the answer is $\frac{3}{12}=\boxed{\text{(B)}\ \frac14}$.

~sakshamsethi

## Video Solution

https://youtu.be/ysNxyATCxzg - Happytwin

## See Also

 2002 AMC 8 (Problems • Answer Key • Resources) Preceded byProblem 24 Followed byLast 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

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