# 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 has $5$. Using the information given in the problem, we can conclude that 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 $\frac{3}{$ (Error compiling LaTeX. ! File ended while scanning use of \frac .)4+3+2+3$}$ (Error compiling LaTeX. ! Extra }, or forgotten \$.) 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