AMC10 2008 B

AMC10 2008 B · Q12

AMC10 2008 B · Q12. It mainly tests Rounding & estimation, Money / coins.

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?

邮递员皮特有一个计步器来记录他的步数。计步器最多记录到 99999 步，然后下一步就翻转到 00000。皮特计划计算一年的里程。1 月 1 日皮特将计步器设为 00000。在一年中，计步器从 99999 翻转到 00000 共 44 次。12 月 31 日计步器显示 50000。皮特每英里走 1800 步。以下哪项最接近皮特一年走的英里数？

(A) 2500 2500

(B) 3000 3000

(D) 4000 4000

(E) 4500 4500

Answer

Correct choice: (A)

正确答案：（A）

Solution

Answer (A): During the year Pete takes $44\times 10^{5}+5\times 10^{4}=44.5\times 10^{5}$ steps. At 1800 steps per mile, the number of miles Pete walks is $\dfrac{44.5\times 10^{5}}{18\times 10^{2}}=\dfrac{44.5}{18}\times 10^{3}\approx 2.5\times 10^{3}=2500.$

答案（A）：在这一年里，Pete 走了 $44\times 10^{5}+5\times 10^{4}=44.5\times 10^{5}$ 步。按每英里 1800 步计算，Pete 走的英里数为 $\dfrac{44.5\times 10^{5}}{18\times 10^{2}}=\dfrac{44.5}{18}\times 10^{3}\approx 2.5\times 10^{3}=2500.$

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