2008 AMC 10B Problem 12

Problem 12 of 25IntermediateAlgebra Number Theory

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

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?

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Solution

Each flip counts

100000

steps, so Pete took

44\cdot 100000+50000=4{,}450{,}000

steps. Dividing by

1800

gives about

2472

miles, which is closest to

2500.

Thus, the correct answer is A.