Question

Paula 钱包中所有一美分、五美分、十美分和二十五美分硬币的平均币值是 $20$ 美分。如果她再有一枚二十五美分硬币，平均币值会变成 $21$ 美分。她的钱包中有多少枚十美分硬币？

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：平均数一次方程

难度评级：1420

解答：

如果 Paula 有 $n$ 枚硬币，它们的总币值是 $20n$ 美分。加入一枚硬币后有 $n + 1$ 枚，总币值为 $20n + 25$ 也等于 $21(n + 1)$ 。

因此 $20n + 25 = 21(n + 1)$ ，解得 $n = 4$ 。

这四枚硬币合计 $80$ 美分，只能是三枚二十五美分硬币和一枚五美分硬币，所以十美分硬币的数量为 $0$ 。

所以正确答案是 A。

If Paula has $n$ coins, their total value is $20n$ cents. Adding a quarter gives $n + 1$ coins worth $20n + 25$ cents, which must also equal $21(n + 1)$ cents.

So $20n + 25 = 21(n + 1),$ giving $n = 4.$

Four coins totalling $80$ cents must be three quarters and one nickel, so the number of dimes is $0.$

Thus, the correct answer is A.

2004 AMC 12A 第 11 题

答案：A

难度评级：1420

解答：

其他年份的第 11 题