AMC12 2010 A

AMC12 2010 A · Q2

AMC12 2010 A · Q2. It mainly tests Averages (mean), Arithmetic sequences basics.

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?

一艘渡船从上午 10 点开始每小时运送游客到一个岛上，直到最后一趟在下午 3 点出发。某天船长注意到上午 10 点那趟船上有 100 名游客，并且之后每一趟的游客人数都比前一趟少 1 人。那天渡船一共把多少名游客送到了岛上？

(A) 585 585

(B) 594 594

(D) 679 679

(E) 694 694

Answer

Correct choice: (A)

正确答案：（A）

Solution

It is easy to see that the ferry boat takes $6$ trips total. The total number of people taken to the island is \begin{align*}&100+99+98+97+96+95\\ &=6(100)-(1+2+3+4+5)\\ &=600 - 15\\ &=\boxed{585\ \textbf{(A)}}\end{align*}

不难看出渡船一共出发 $6$ 趟。送到岛上的总人数为 \begin{align*}&100+99+98+97+96+95\\ &=6(100)-(1+2+3+4+5)\\ &=600 - 15\\ &=\boxed{585\ \textbf{(A)}}\end{align*}

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