2022 AMC 8 第 11 题

先试着解答 2022 AMC 8 第 11 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 2022 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。

11.

驴 Henry 有一根很长的意大利面。他咬了若干口,每次都从某一段意大利面的中间吃掉 33 英寸。最后他有 1010 段意大利面,总长度为 1717 英寸。他最开始的那根意大利面长多少英寸?
Henry the donkey has a very long piece of pasta. He takes a number of bites of pasta, each time eating 33 inches of pasta from the middle of one piece. In the end, he has 1010 pieces of pasta whose total length is 1717 inches. How long, in inches, was the piece of pasta he started with?
3434
3838
4141
4444
4747
答案:D
知识点:不变量
小提示:
每咬一口,意大利面段数增加 11
Each bite increases the number of pasta pieces by 11
大提示:
最后有 1010 段,所以 Henry 咬了 99 口
To end with 1010 pieces, Henry made 99 bites
解答:
从一整段变成 1010 段,需要咬 99 口。咬了 99 口,每口吃掉 33 英寸,所以共吃掉 2727 英寸。
已经吃掉 2727 英寸,最后还剩 1717 英寸,因此原长为 27+17=4427+17 = 44 英寸。
正确答案是 D。
Since there are 1010 pieces, there were 99 locations where a bite was made. Since we have 99 bites and 33 inches are removed per bite, a total of 2727 inches were removed.
With 2727 inches removed and 1717 inches remaining, we know we started with 27+17=4427+17 = 44 inches.
Thus, the correct answer is D.
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