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

解答：

若有 $n$ 枚硬币，总面值为 $20n$ 美分。方程给出 $n = 4$ 。 $20n + 25 = 21(n + 1),$

四枚硬币总值 $10$ 美分，只能是三枚二十五分硬币和一枚五分硬币。因此十分硬币的数量为 $0$ 。 $2(25)+2(10)=70$ $5$

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

解答：

其他年份的第 14 题