AMC 10 Weekly Practice Round 2

Complete problem set with solutions and individual problem pages

Problem 7 Medium

In a garage, there are some two-wheeled motorcycles and four-wheeled cars. The ratio of the number of vehicles to the number of wheels is 2:5.

What is the ratio of the number of motorcycles to the number of cars?

  • A.

    3:1

  • B.

    1:3

  • C.

    4:1

  • D.

    1:4

  • E.

    3:2

Answer:A

Let there be x motorcycles and y cars.

According to the problem: x + y = \frac{2}{5}(2x + 4y)

Multiply both sides by 5: 5x + 5y = 4x + 8y

Solving gives: x = 3y

Therefore, the ratio of motorcycles to cars is x : y = 3 : 1

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