AMC 8 Daily Practice Round 8

Complete problem set with solutions and individual problem pages

Problem 13 Medium

There are 3 classes in the sixth grade of a certain elementary school. It is known that: the sum of the average number of students in Class 1 and Class 2 and the number of students in Class 3 is 48, the sum of the average number of students in Class 2 and Class 3 and the number of students in Class 1 is 50, the sum of the average number of students in Class 1 and Class 3 and the number of students in Class 2 is 52. What is the total number of students in the three classes?

  • A.

    70

  • B.

    72

  • C.

    74

  • D.

    75

  • E.

    77

Answer:D

\frac{1}{2} \times (\text{Class 1} + \text{Class 2}) + \text{Class 3} = 48 ①

\frac{1}{2} \times (\text{Class 2} + \text{Class 3}) + \text{Class 1} = 50 ②

\frac{1}{2} \times (\text{Class 1} + \text{Class 3}) + \text{Class 2} = 52 ③

Adding equations ①, ②, and ③ gives:

2 \times (\text{Class 1} + \text{Class 2} + \text{Class 3}) = 150

Therefore: \text{Class 1} + \text{Class 2} + \text{Class 3} = 75

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