Question

邮差 Pete 有一个计步器来记录步数。计步器最多显示 $99999$ 步，下一步会翻转为 $00000$ 。Pete 计划计算自己一年的里程。一月 $1$ 日，Pete 将计步器设为 $00000$ 。一年中，计步器从 $99999$ 翻到 $00000$ 共四十四次。十二月 $31$ 日，计步器显示 $50000$ 。Pete 每英里走 $1800$ 步。下列哪一项最接近 Pete 这一年走过的英里数？

Postman Pete has a pedometer to count his steps. The pedometer records up to $99999$ steps, then flips over to $00000$ on the next step. Pete plans to determine his mileage for a year. On January $1$ Pete sets the pedometer to $00000.$ During the year, the pedometer flips from $99999$ to $00000$ forty-four times. On December $31$ the pedometer reads $50000.$ Pete takes $1800$ steps per mile. Which of the following is closest to the number of miles Pete walked during the year?

$2500$

$3000$

$3500$

$4000$

$4500$

答案：A

知识点：位值估算单位换算

难度评级：1350

小提示：

计步器每翻转一次代表 $100000$ 步；再加上最后显示的 $50000$ 。

Each flip of the pedometer represents $100000$ steps; add the final reading of $50000$

大提示：

将总步数除以 $1800$ ，换算成英里。

Divide the total number of steps by $1800$ to convert to miles

解答：

每次翻转表示 $100000$ 步，所以这一年的总步数为 $\begin{aligned} &44 \cdot 100000 \\ &\quad {}+ 50000 = 4{,}450{,}000 \end{aligned}\text{。}$

每英里 $1800$ 步，所以里程为 $\dfrac{4{,}450{,}000}{1800} \approx 2472$ ，最接近 $2500$ 。

因此，正确答案是 A。

Each flip counts $100000$ steps, so the year’s steps total $\begin{aligned} &44 \cdot 100000 \\ &\quad {}+ 50000 = 4{,}450{,}000. \end{aligned}$

At $1800$ steps per mile, the mileage is $\dfrac{4{,}450{,}000}{1800} \approx 2472,$ which is closest to $2500.$

Thus, the correct answer is A.

2008 AMC 12B 第 6 题

答案：A

难度评级：1350

小提示：

大提示：

解答：

其他年份的第 6 题