2010 AMC 12A 第 2 题

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

小提示：

数一数从上午

10

点到下午

3

点一共有多少班。

Count how many trips run from

10

am through

3

pm

大提示：

各班人数为

100,99,\ldots,95

；把它们相加。

The trip counts are

100,99,\ldots,95;

add them

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}\text{。}

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

小提示：

大提示：

解答：

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