Try this beautiful problem from AMC-8, 2002 related to money (problem 25).
Problem related to Money – AMC-8, 2002 – 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:\(\frac{1}{4}\)
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 =\(\frac{3y}{12y} = \frac{1}{4}\)
Other useful links
- https://www.youtube.com/watch?v=_HYhADRACPs
- https://www.cheenta.com/prime-numbers-amc-8-2006-problem-25/
Related Program
AMC – AIME Boot Camp… for brilliant students.
Use our exclusive one-on-one plus group class system to prepare for Math Olympiad
Good