The average weight of students in a class of 35 students is 40 kg. If the weight of the teacher is included, then the average raises by `(1)/(3)` kg. The weight of the teacher is

Options

A. 40.5 kg
B. 50 kg
C. 41 kg
D. 52 kg

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Calculate the total weight of the students
Given that the average weight of 35 students is 40 kg, we can calculate the total weight of the students.

\[ \text{Total weight of students} = \text{Average weight} \times \text{Number of students} = 40 \, \text{kg} \times 35 = 1400 \, \text{kg} \]

**Hint:** Use the formula for average to find the total weight by multiplying the average by the number of individuals.

### Step 2: Set up the equation for the new average including the teacher
When the teacher's weight is included, the average weight increases by \( \frac{1}{3} \) kg. Therefore, the new average weight becomes:

\[ \text{New average} = 40 \, \text{kg} + \frac{1}{3} \, \text{kg} = \frac{120}{3} + \frac{1}{3} = \frac{121}{3} \, \text{kg} \]

Now, the total number of individuals (students + teacher) is 36. We can express the total weight including the teacher's weight \( T \):

\[ \text{Total weight including teacher} = 1400 \, \text{kg} + T \]

The equation for the new average can be set up as:

\[ \frac{1400 + T}{36} = \frac{121}{3} \]

**Hint:** When including a new individual, remember to adjust the total number of individuals and set up the equation for the new average.

### Step 3: Solve for the teacher's weight
Now, we can multiply both sides of the equation by 36 to eliminate the fraction:

\[ 1400 + T = 36 \times \frac{121}{3} \]

Calculating the right side:

\[ 36 \times \frac{121}{3} = 12 \times 121 = 1452 \]

Now we have:

\[ 1400 + T = 1452 \]

Subtracting 1400 from both sides gives:

\[ T = 1452 - 1400 = 52 \, \text{kg} \]

**Hint:** When solving for a variable, isolate it on one side of the equation by performing inverse operations.

### Conclusion
The weight of the teacher is \( 52 \, \text{kg} \).

**Final Answer:** The weight of the teacher is \( 52 \, \text{kg} \).