The mean weight of 34 students is 42 kg. Including the teacher raises the mean by 0.4 kg (400 g). What is the teacher's weight?

Introduction / Context:
When one more person is added and the average changes by a known amount, compute the new total (using the new average and new headcount) and subtract the old total to get the added person's value.

Given Data / Assumptions:

• Students: 34; mean = 42 kg.
• Including teacher: 35 people; mean = 42.4 kg.
• Find teacher's weight.

Concept / Approach:
Let T_students be total of students; T_all be total including teacher. Teacher weight = T_all − T_students.

Step-by-Step Solution:

Verification / Alternative check:
Check resulting mean: (1428 + 56) / 35 = 1484 / 35 = 42.4, which matches the stated increase.

Why Other Options Are Wrong:
66, 55, 57: Do not match the exact difference between new and old totals.

Common Pitfalls:
Applying the 0.4 kg increase to only one person directly (which would be wrong) instead of recalculating totals across the new headcount.

Final Answer:
56