2008 AMC 10B Problems/Problem 12

Problem

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?

$\mathrm{(A)}\ 2500\qquad\mathrm{(B)}\ 3000\qquad\mathrm{(C)}\ 3500\qquad\mathrm{(D)}\ 4000\qquad\mathrm{(E)}\ 4500$

Solution

Every time the pedometer flips from $99999$ to

$00000$ Pete has walked $100000$ steps.

So, if the pedometer flipped $44$ times

Pete walked $44*100000+50000=4450000$ steps.

Dividing by $1800$ steps per mile gives $2472.\overline{2}$

This is closest to answer $\boxed{A}$ .

2008 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 11	Followed by Problem 13
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2008 AMC 10B Problems/Problem 12

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