Difference between revisions of "2002 AMC 8 Problems/Problem 25"
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− | Assume Moe has <math>\$ 5</math> | + | 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>. |
~sakshamsethi | ~sakshamsethi |
Revision as of 18:53, 14 July 2020
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?
Solution
Since Ott gets equal amounts of money from each friend, we can say that he gets dollars from each friend. This means that Moe has dollars, Loki has dollars, and Nick has dollars. The total amount is dollars, and since Ott gets dollars total, .
Solution 2 (easiest)
Assume Moe, Loki, and Nick each give Ott . Therefore, Moe has , Loki has , and Nick has . After everyone gives Ott some fraction of their money, he gets . reviewing the situation, Moe now has , Loki has , and Nick has . Ott has fraction of the group's money. Thus, the answer is .
~sakshamsethi
Video Solution
https://youtu.be/ysNxyATCxzg - Happytwin
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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