2006 AMC 8 第 15 题

先试着解答 2006 AMC 8 第 15 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 2006 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。

15.

Chandra 和 Bob 各有一本书,他们决定用“团队阅读”来节省时间。按照这种方法,Chandra 从第 11 页读到某一页,Bob 从下一页读到第 760760 页,读完整本书。读完后他们会互相讲述自己读的部分。为了让 Chandra 和 Bob 阅读时间相同,Chandra 应该读到最后哪一页?
Chandra and Bob, who each have a copy of the book, decide that they can save time by “team reading” the novel. In this scheme, Chandra will read from page 11 to a certain page and Bob will read from the next page through page 760,760, finishing the book. When they are through they will tell each other about the part they read. What is the last page that Chandra should read so that she and Bob spend the same amount of time reading the novel?
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答案:C
知识点:速率一次方程
小提示:
设 xx 为 Chandra 阅读的页数。
Let xx be the number of pages Chandra reads.
大提示:
令 Chandra 阅读 xx 页的时间等于 Bob 阅读剩余页数的时间。
Set Chandra’s time for xx pages equal to Bob’s time for the remaining pages.
解答:
设 Chandra 阅读 xx 页,那么 Bob 阅读 760−x760 - x 页。
为了让阅读时间相同,30x=45(760−x)30x=45⋅760−45x75x=45⋅7605x=3⋅760x=3⋅152x=456。 \begin{align*} 30x &= 45(760 - x) \\ 30x &= 45 \cdot 760 - 45x \\ 75x &= 45 \cdot 760 \\ 5x &= 3 \cdot 760 \\ x &= 3 \cdot 152 \\ x &= 456 \end{align*}\text{。}
所以正确答案是 C。
Let xx be the number of pages that Chandra will read. Then Bob will read 760−x760 - x pages.
For them to read for the same amount of time, 30x=45(760−x)30x=45⋅760−45x75x=45⋅7605x=3⋅760x=3⋅152x=456. \begin{align*} 30x &= 45(760 - x) \\ 30x &= 45 \cdot 760 - 45x \\ 75x &= 45 \cdot 760 \\ 5x &= 3 \cdot 760 \\ x &= 3 \cdot 152 \\ x &= 456. \end{align*}
Thus, C is the correct answer.
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