Understanding the Average Weight Problem
This problem asks us to find the weight of a teacher who replaces a student in a class. We know the initial number of students, the weight of the student who left, and how the average weight of the class changed after the replacement.
Calculating the Total Weight Change
Let's break down how the total weight changes when the student is replaced by the teacher.
- Initial Situation: We have 35 students with an average weight.
- Change: One student weighing 35 kg is removed, and a teacher is added. The number of people remains 35.
- Impact: The average weight increases by 2 kg.
An increase in the average weight means the total weight of the group must have increased. Since the number of people (35) stayed the same, the total increase in weight must be equal to the increase in the average weight multiplied by the number of people.
Total increase in weight = (Increase in average weight) × (Number of people)
Total increase in weight = $2 \text{ kg} \times 35 = 70 \text{ kg}$
Determining the Teacher's Weight
The total weight increase of 70 kg is the difference between the teacher's weight and the weight of the student who was replaced.
Total increase in weight = Weight of Teacher - Weight of Replaced Student
We know the total increase is 70 kg and the weight of the replaced student is 35 kg.
So, $70 \text{ kg} = \text{Weight of Teacher} - 35 \text{ kg}$
To find the weight of the teacher, we rearrange the equation:
Weight of Teacher = $70 \text{ kg} + 35 \text{ kg}$
Weight of Teacher = $105 \text{ kg}$
Step-by-Step Solution Summary
- Calculate the total increase in weight for the class: $2 \text{ kg/student} \times 35 \text{ students} = 70 \text{ kg}$.
- This total increase is the difference between the new person's weight (teacher) and the old person's weight (student).
- Add the weight difference to the replaced student's weight to find the teacher's weight: $35 \text{ kg} + 70 \text{ kg} = 105 \text{ kg}$.
Conclusion
The weight of the teacher is 105 kg.
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