Question

Paula 钱包中所有一分、五分、十分和二十五分硬币的平均面值是 $20$ 美分。如果她再多一枚二十五分硬币，平均面值会变为 $21$ 美分。她钱包中有多少枚十分硬币？

The average value of all the pennies, nickels, dimes, and quarters in Paula’s purse is $20$ cents. If she had one more quarter, the average value would be $21$ cents. How many dimes does she have in her purse?

$0$

$1$

$2$

$3$

$4$

答案：A

知识点：平均数钱币一次方程

难度评级：1450

小提示：

若她有 $n$ 枚硬币，总面值为 $20n$ 美分。

If she has $n$ coins, their total value is $20n$ cents

大提示：

加一枚二十五分硬币后， $20n + 25 = 21(n + 1)$ 。

Adding a quarter gives $20n + 25 = 21(n + 1)$

解答：

若有 $n$ 枚硬币，总面值为 $20n$ 美分。加一枚二十五分硬币后，方程为 $20n + 25 = 21(n + 1)\text{，}$ 解得 $n = 4$ 。

如果二十五分硬币至多有两枚，其余硬币每枚最多值 $10$ 美分，那么四枚硬币的总值至多为 $2(25)+2(10)=70$ 美分。因此必须有三枚二十五分硬币，第四枚硬币的面值为 $5$ 美分。钱包中有三枚二十五分硬币和一枚五分硬币，所以十分硬币有 $0$ 枚。

所以正确答案是 A。

With $n$ coins the total value is $20n$ cents. Adding a quarter gives $20n + 25 = 21(n + 1),$ so $n = 4.$

If there were at most two quarters, the other coins would be worth at most $10$ cents each, so four coins would total at most $2(25)+2(10)=70$ cents. Thus there must be three quarters, leaving $5$ cents for the fourth coin. The purse contains three quarters and one nickel, so it has $0$ dimes.

Thus, the correct answer is A.

2004 AMC 10A 第 14 题

答案：A

难度评级：1450

小提示：

大提示：

解答：

其他年份的第 14 题