AMC 10 Daily Practice Round 3

Complete problem set with solutions and individual problem pages

Problem 1 Easy

Mei can travel to her grandma's house by a direct route, or by a scenic route that is 5\ \text{km} longer. When she travels by the scenic route, and comes directly home, the round trip is 35\ \text{km}. How long is the direct route?

  • A.

    5\ \text{km}

  • B.

    12.5\ \text{km}

  • C.

    15\ \text{km}

  • D.

    20\ \text{km}

  • E.

    22.5\ \text{km}

Answer:C

Let the length of the direct route be x kilometers, so the length of the scenic route is x + 5 kilometers. When Mei chooses the scenic route to her grandmother's house and then directly returns home, the total round trip includes the scenic route on the way there and the direct route on the way back. Therefore, the total length can be represented as: (x + 5) + x = 35. Solve this equation, x = 15. So, the length of the direct route is 15 kilometers.

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