1992 AMC 8 Problem 12

Below is the professionally curated solution for Problem 12 of the 1992 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1992 AMC 8 solutions, or check the answer key.

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Concepts:rate

Difficulty rating: 980

12.

The five tires of a car (four road tires and a full-sized spare) were rotated so that each tire was used the same number of miles during the first $30{,}000$ miles the car traveled. For how many miles was each tire used?

$6000$

$7500$

$24{,}000$

$30{,}000$

$37{,}500$

Solution:

During the $30{,}000$ miles, $4$ tires are always in use, so the total tire-mileage is $4 \times 30{,}000 = 120{,}000$ tire-miles.

Split equally among $5$ tires, each tire is used $\dfrac{120{,}000}{5} = 24{,}000$ miles.

Thus, the correct answer is C .

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