Calculate Teacher's Weight
We need to find the teacher's weight given the initial average weight of students and the new average weight after including the teacher.
Initial Calculation
The initial group consists of 10 students with an average weight of 50 kg.
- Number of students: $10$
- Average weight of students: $50 \text{ kg}$
- Total weight of students: $10 \times 50 \text{ kg} = 500 \text{ kg}$
Calculation with Teacher Included
When the teacher is included, the group size increases, and the average weight also increases.
- New number of people (students + teacher): $10 + 1 = 11$
- The average weight increases by 1 kg: New average weight = $50 \text{ kg} + 1 \text{ kg} = 51 \text{ kg}$
- New total weight of the group (students + teacher): $11 \times 51 \text{ kg} = 561 \text{ kg}$
Determine Teacher's Weight
The teacher's weight is the difference between the new total weight and the initial total weight of the students.
- Teacher's weight = New total weight - Total weight of students
- Teacher's weight = $561 \text{ kg} - 500 \text{ kg}$
- Teacher's weight = $61 \text{ kg}$
Therefore, the teacher's weight is 61 kg.
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