The average weight of a class of 33 students is 47 kg. If the weight of the teacher is included, then the average weight of the class increases by 1 kg. What is the weight of the teacher?
Question
The average weight of a class of 33 students is 47 kg. If the weight of the teacher is included, then the average weight of the class increases by 1 kg. What is the weight of the teacher?
Solution
Step 1: Calculate the total weight of the 33 students.
The average weight of the 33 students is 47 kg, so the total weight is 33 students * 47 kg/student = 1561 kg.
Step 2: Calculate the new average weight when the teacher is included.
The average weight increases by 1 kg when the teacher is included, so the new average weight is 48 kg.
Step 3: Calculate the total weight of the 33 students and the teacher.
The total weight is now the number of students plus the teacher (33 + 1 = 34) times the new average weight, or 34 * 48 kg = 1632 kg.
Step 4: Subtract the total weight of the 33 students from the total weight of the 33 students and the teacher to find the weight of the teacher.
The weight of the teacher is 1632 kg - 1561 kg = 71 kg.
So, the teacher weighs 71 kg.
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