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 1

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, $\frac{3x}{12x}= \frac{3}{12} = \boxed{\text{(B)}\ \frac14}$.

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.

$5\cdot3=15$ which is the total money the group gave Ott.

$25+20+15=60$ is the group's balance. Therefore, the fraction of the group's money that Ott now has is $\frac{15}{60} = \boxed{\text{(B)}\ \frac14}$.

Video Solution

https://www.youtube.com/watch?v=F-ZvPoJdnfk ~David

See Also

2002 AMC 8 (ProblemsAnswer KeyResources)
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