The mean weight of a class of 34 students is 46.5 kg. If the weight of the teacher is included, the mean rises by 500 g. Then the weight of the teacher is________.

Options

A. 175 kg
B. 62 kg
C. 64 kg
D. 72 kg

Answer

To find the weight of the teacher, we can follow these steps:

### Step 1: Calculate the total weight of the students
Given that the mean weight of 34 students is 46.5 kg, we can calculate the total weight of the students using the formula:

\[ \text{Total weight of students} = \text{Number of students} \times \text{Mean weight} \]

\[ \text{Total weight of students} = 34 \times 46.5 = 1581 \text{ kg} \]

### Step 2: Determine the new mean weight when the teacher is included
When the teacher's weight is included, the mean weight increases by 500 grams (or 0.5 kg). Therefore, the new mean weight is:

\[ \text{New mean} = 46.5 + 0.5 = 47 \text{ kg} \]

### Step 3: Set up the equation for the total weight including the teacher
Now, when the teacher is included, the total number of individuals (students + teacher) becomes 35. The formula for the new mean is:

\[ \text{New mean} = \frac{\text{Total weight of students} + \text{Weight of teacher}}{\text{Total number of individuals}} \]

Substituting the known values:

\[ 47 = \frac{1581 + \text{Weight of teacher}}{35} \]

### Step 4: Solve for the weight of the teacher
To find the weight of the teacher, we can rearrange the equation:

\[ 47 \times 35 = 1581 + \text{Weight of teacher} \]

Calculating \(47 \times 35\):

\[ 1645 = 1581 + \text{Weight of teacher} \]

Now, isolate the weight of the teacher:

\[ \text{Weight of teacher} = 1645 - 1581 = 64 \text{ kg} \]

### Final Answer
The weight of the teacher is **64 kg**.

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