Answer and Step-by-step explanation:
Let's solve this problem step by step:
Let's assume that the initial number of students in the class is "x".
Given:
Average weight of the students in the class = 60 kg
Average weight of the new students = 64 kg
Average weight of the entire class after the new students join = 62 kg
Step 1: Calculate the total weight of the students in the class initially.
Total weight of the students in the class initially = Average weight * Number of students
Total weight of the students in the class initially = 60 kg * x
Step 2: Calculate the total weight of the new students.
Total weight of the new students = Average weight of the new students * Number of new students
Total weight of the new students = 64 kg * 8
Step 3: Calculate the total weight of the entire class after the new students join.
Total weight of the entire class after the new students join = Average weight of the entire class after the new students join * Total number of students in the class after the new students join
Total weight of the entire class after the new students join = 62 kg * (x + 8)
Step 4: Set up the equation.
According to the given information, the total weight of the students in the class initially plus the total weight of the new students should be equal to the total weight of the entire class after the new students join.
60 kg * x + 64 kg * 8 = 62 kg * (x + 8)
Step 5: Solve the equation to find the value of "x".
60x + 512 = 62x + 496
2x = 16
x = 8
Therefore, the initial number of students in the class was 8.