2008 AMC 12B Problem 6

Problem 6 of 25EasierAlgebra 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 the year’s steps total

\begin{aligned} &44 \cdot 100000 \\ &\quad {}+ 50000 = 4{,}450{,}000. \end{aligned}

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.