AMC 8 2002 Problem 25
AMC8 2002 年第 25 题
比与比例★★★☆☆
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?
Loki，Moe，Nick 和 Ott 是好朋友。Ott 没有钱，但其他人有。Moe 给了 Ott 五分之一的钱， Loki 给了 Ott 四分之一的钱，Nick 给了 Ott 三分之一的钱。每个人都给了 Ott 同样的钱。那么现在 Ott 有的钱占了四个人全部的钱的几分之几？
- A.
- B.
- C.
- D.
- E.
正确答案 · Correct Answer
B
解析 · Solution
Solution 1
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, .
We can assign any natural number to the price that Ott's friends gave him. For this example, we will use 5. Moe gave Ott a fifth of his money, and also five dollars, so in total Moe has 25 dollars. Loki gave Ott a fourth of his money, and also five dollars, so in total Loki has 20 dollars. Nick gave Ott a third of his money, and also five dollars, so in total Nick has 15 dollars. is the total money the group gave Ott. 25+20+15 = 60 is the group's balance. Therefore, the fraction of the group's money that Ott now has is .
继续练习