The average weight of 6 techers in a school is 47.3 kg. When a new teacher joined them, the average weight is increased by 5.3 kg . Then find the approximate weight of the new teacher.

Options

A. 70 kg
B. 84 kg
C. 60 kg
D. 78 kg

Explanation

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

### Step 1: Calculate the total weight of the 6 teachers.
The average weight of the 6 teachers is given as 47.3 kg. To find the total weight, we can use the formula:

\[ \text{Total Weight} = \text{Average Weight} \times \text{Number of Teachers} \]

Substituting the values:

\[ \text{Total Weight} = 47.3 \, \text{kg} \times 6 = 283.8 \, \text{kg} \]

### Step 2: Determine the new average weight after the new teacher joins.
When a new teacher joins, the average weight increases by 5.3 kg. Therefore, the new average weight is:

\[ \text{New Average Weight} = 47.3 \, \text{kg} + 5.3 \, \text{kg} = 52.6 \, \text{kg} \]

### Step 3: Set up the equation for the total weight with the new teacher.
Now, with the new teacher, the total number of teachers becomes 7. The total weight with the new teacher can be expressed as:

\[ \text{Total Weight with New Teacher} = \text{Total Weight of 6 Teachers} + \text{Weight of New Teacher} \]

Let the weight of the new teacher be \( X \). Thus, we can write:

\[ 283.8 \, \text{kg} + X = 52.6 \, \text{kg} \times 7 \]

### Step 4: Calculate the total weight for 7 teachers.
Now, we calculate the total weight for the 7 teachers:

\[ \text{Total Weight for 7 Teachers} = 52.6 \, \text{kg} \times 7 = 368.2 \, \text{kg} \]

### Step 5: Solve for the weight of the new teacher \( X \).
Now, we can substitute back into our equation:

\[ 283.8 \, \text{kg} + X = 368.2 \, \text{kg} \]

To find \( X \), we rearrange the equation:

\[ X = 368.2 \, \text{kg} - 283.8 \, \text{kg} \]

Calculating this gives:

\[ X = 84.4 \, \text{kg} \]

### Step 6: Approximate the weight of the new teacher.
Since we need the approximate weight, we can round \( 84.4 \, \text{kg} \) to the nearest whole number:

\[ \text{Approximate Weight of New Teacher} \approx 84 \, \text{kg} \]

### Final Answer:
The approximate weight of the new teacher is **84 kg**.

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