AMC 10 Weekly Practice Round 2

Complete problem set with solutions and individual problem pages

Problem 9 Medium

The ratio of the number of students participating in a math competition from School A and School B is 7:8, and the ratio of the number of students who won awards is 2:3. Each school has 240 students who did not win an award. How many students participated in the competition in total?

  • A.

    650

  • B.

    680

  • C.

    720

  • D.

    760

  • E.

    780

Answer:C

Let the number of students participating from School A and School B be 7x and 8x respectively.

According to the problem, the number of students who did **not** win awards in each school is: (7x - 240) : (8x - 240) = 2 : 3

Solving the equation gives: x = 48

Therefore, the total number of participants from both schools is: 7x + 8x = 15x = 720 students.

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