Multiple choice

There are 60 students in a class. The average weight of the class increased by 200 g when a student weighing 45 kg left the class. What is the average weight of the remaining students?

  1. 57 kg

  2. 56.8 kg

  3. 58.2 kg

  4. 54 kg

  5. 52.3 kg
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A Correct answer
Explanation

Let the initial average be A. The total weight is 60A. After a 45 kg student leaves, the total weight is 60A - 45, and the new average is (60A - 45)/59. We are given (60A - 45)/59 = A + 0.2. Solving for A: 60A - 45 = 59A + 11.8, so A = 56.8 kg. The new average is 56.8 + 0.2 = 57 kg.

AI explanation

Let the initial average weight of the 60 students be x. When the 45 kg student leaves, the remaining 59 students have an average weight of x plus 0.2 kg. The total weight before the student leaves is 60x, and the total weight after is 59 times x plus 0.2, which equals 59x plus 11.8. Setting the difference equal to the departing student's weight gives 60x minus 59x minus 11.8 equals 45, so x is 56.8 kg. The average weight of the remaining students is 56.8 plus 0.2, resulting in 57 kg.

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