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2014 AMC 10B Problem 3

Problem 3 of 25EasierAlgebraArithmetic

Randy drove the first third of his trip on a gravel road, the next 2020 miles on pavement, and the remaining one-fifth on a dirt road. In miles, how long was Randy’s trip?

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Solution

Let the path distance be t.t. Then, we get: t=t5+20+t3t=20+8t15715t=20t=3007.\begin{aligned}t &= \dfrac t5 + 20 + \dfrac t3 \\ t &= 20 + \dfrac {8t}{15} \\ \dfrac 7{15} t &= 20\\ t &= \dfrac{300}7.\end{aligned} Thus, the correct answer is E .
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