2014 AMC 12B Problem 3

Below is the professionally curated solution for Problem 3 of the 2014 AMC 12B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2014 AMC 12B solutions, or check the answer key.

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Concepts:fraction linear equation

Difficulty rating: 1150

Randy drove the first third of his trip on a gravel road, the next $20$ miles on pavement, and the remaining one-fifth on a dirt road. In miles, how long was Randy's trip?

$30$

$\dfrac{400}{11}$

$\dfrac{75}{2}$

$40$

$\dfrac{300}{7}$

Solution:

The fraction of the trip on pavement is $1 - \tfrac13 - \tfrac15 = \tfrac{7}{15}.$

Since this equals $20$ miles, the whole trip is $20 \div \tfrac{7}{15} = \tfrac{300}{7}$ miles.

Thus, the correct answer is E.

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