Question

一艘渡船从上午 $10$ 点开始，每小时载游客去一座岛，最后一班在下午 $3$ 点出发。某天船长注意到上午 $10$ 点那班有 $100$ 名游客，并且之后每一班的游客数都比前一班少 $1$ 人。那天这艘渡船一共载了多少名游客到岛上？

A ferry boat shuttles tourists to an island every hour starting at $10$ am until its last trip, which starts at $3$ pm. One day the boat captain notes that on the $10$ am trip there were $100$ tourists on the ferry boat, and that on each successive trip, the number of tourists was $1$ fewer than on the previous trip. How many tourists did the ferry take to the island that day?

$585$

$594$

$672$

$679$

$694$

答案：A

知识点：等差数列求和

难度评级：970

解答：

渡船共有 $6$ 班： $10$ 点、 $11$ 点、 $12$ 点、 $1$ 点、 $2$ 点和 $3$ 点。

游客数分别为 $100,99,98,97,96,95$ ，所以总数为 $\begin{gathered} 6\cdot100-(1+2+3+4+5) \\ =600-15 \\ =585. \end{gathered}$

所以正确答案是 A。

The ferry makes $6$ trips: at $10,$ $11,$ $12,$ $1,$ $2,$ and $3.$

The numbers of tourists are $100,99,98,97,96,95,$ so the total is $\begin{gathered} 6\cdot100-(1+2+3+4+5) \\ =600-15 \\ =585. \end{gathered}$

Thus, A is the correct answer.

2010 AMC 12A 第 2 题

答案：A

难度评级：970

解答：

其他年份的第 2 题