2004 AMC 8 第 9 题

先试着解答 2004 AMC 8 第 9 题,然后核对你的答案与精心整理的解答,解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2004 AMC 8 解答,或核对答案。

所有题目均经美国数学协会(MAA)官方合法授权使用。

9.

一个列表中五个数的平均数是 5454。前两个数的平均数是 4848。后三个数的平均数是多少?
The average of the five numbers in a list is 54.54. The average of the first two numbers is 48.48. What is the average of the last three numbers?
5555
5656
5757
5858
5959
答案:D
知识点:平均数
小提示:
把每个平均数转化为总和
Turn each average into a sum.
大提示:
从五个数总和中减去前两个数的总和
Subtract the sum of the first two numbers from the sum of all five.
解答:
55 个数的总和是 54⋅5=27054 \cdot 5 = 270。前 22 个数的总和是 48⋅2=9648 \cdot 2 = 96。
后 33 个数的总和是 270−96=174270 - 96 = 174,所以平均数是 174÷3=58174 \div 3 = 58。
所以正确答案是 D。
The sum of all 55 numbers is 54⋅5=270.54 \cdot 5 = 270. The sum of the first 22 numbers is 48⋅2=96.48 \cdot 2 = 96.
The sum of the last 33 numbers is 270−96=174.270 - 96 = 174. The average is therefore 174÷3=58.174 \div 3 = 58.
Thus, D is the correct answer.
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