Try this beautiful problem from AMC-8, 2002 related to money (problem 25).


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?

  • \(\frac{1}{3}\)
  • \(\frac{1}{4}\)
  • \(\frac{3}{4}\)

Key Concepts


Algebra

Number theory

fraction

Check the Answer


But try the problem first…

Answer:\(\frac{1}{4}\)

Source
Suggested Reading

AMC-8 (2002) Problem 25

Challenges and Thrills in Pre College Mathematics

Try with Hints


First hint

Each Friend gave Ott the equal amount of money

Can you now finish the problem ……….

Second Hint

Assume that ott gets y dollars from each friend

Can you finish the problem……..

Final Step

 

Given that Ott gets equal amounts of money from each friend,
we can say that he gets y dollars from each friend.
This means that Moe has 5y dollars,
Loki has 4y dollars, and Nick has 3y dollars.
The total amount is 12y dollars,
Therefore Ott gets 3y dollars total,
Required fraction =\(\frac{3y}{12y} = \frac{1}{4}\)

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