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2002 AMC 8 Problems/Problem 25

Revision as of 19:04, 15 April 2023 by Supermathking (talk | contribs) (→‎Video Solution)

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, the total money at the end situation will be the same as the original; which is $$ 12$. Ott gets $$ 1$ $+$ $$ 1$ $+$ $$ 1$ $=$ $$ 3$. Thus, the answer is $\frac{3}{12}=\boxed{\text{(B)}\ \frac14}$.

~sakshamsethi

Video Solution

https://youtu.be/ysNxyATCxzg - Happytwin

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

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)
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All AJHSME/AMC 8 Problems and Solutions

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