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Difference between revisions of "2002 AMC 8 Problems/Problem 25"

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Since Ott gets equal amounts of money from each friend, we can say that he gets <math>x</math> dollars from each friend. This means that Moe has <math>5x</math> dollars, Loki has <math>4x</math> dollars, and Nick has <math>3x</math> dollars. The total amount is <math>12x</math> dollars, and since Ott gets <math>3x</math> dollars total, <math>\frac{3x}{12x}= \frac{3}{12} = \boxed{\text{(B)}\ \frac14}</math>.
 
Since Ott gets equal amounts of money from each friend, we can say that he gets <math>x</math> dollars from each friend. This means that Moe has <math>5x</math> dollars, Loki has <math>4x</math> dollars, and Nick has <math>3x</math> dollars. The total amount is <math>12x</math> dollars, and since Ott gets <math>3x</math> dollars total, <math>\frac{3x}{12x}= \frac{3}{12} = \boxed{\text{(B)}\ \frac14}</math>.
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<math>\blacksquare</math>
 
  
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==Video Solution==
  
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==Solution 2 (easiest)==
 
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Assume Moe, Loki, and Nick each give Ott <math>\$ 1</math>. Therefore, Moe has <math>\$ 5</math>, Loki has <math>\$ 4</math>, and Nick has <math>\$ 3</math>. After everyone gives Ott some fraction of their money, he gets <math>\$ 1</math> <math>+</math> <math>\$ 1</math> <math>+</math> <math>\$ 1</math> <math>=</math> <math>\$ 3</math>. reviewing the situation, Moe now has <math>\$ 5</math> <math>-</math> <math>\$ 1</math> <math>=</math> <math>\$ 4</math>, Loki has <math>\$ 4</math> <math>-</math> <math>\$ 1</math> <math>=</math> <math>\$ 3</math>, and Nick has <math>\$ 3</math> <math>-</math> <math>\$ 1</math> <math>=</math> <math>\$ 2</math>. Ott has <math>\frac{3}{4+3+2+3}</math> fraction of the group's money. Thus, the answer is <math>\frac{3}{12}=\boxed{\text{(B)}\ \frac14}</math>.
 
  
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~sakshamsethi
 
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==Video Solution==
 
  
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https://youtu.be/ysNxyATCxzg - Happytwin
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https://www.youtube.com/watch?v=F-ZvPoJdnfk  ~David
  
 
==See Also==
 
==See Also==
 
{{AMC8 box|year=2002|num-b=24|after=Last <br /> Problem}}
 
{{AMC8 box|year=2002|num-b=24|after=Last <br /> Problem}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 09:18, 14 June 2024

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

Video Solution

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

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

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