The average of height of 16 students is 142 cm. If the height of the teacher is included, the average height increases by 1 cm. The height of the teacher is

Options

A. 156 cm
B. 159 cm
C. 158 cm
D. 157 cm

Explanation

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

### Step 1: Calculate the total height of the 16 students.
The average height of the 16 students is given as 142 cm.

To find the total height of the students, we use the formula:
\[ \text{Total Height} = \text{Average Height} \times \text{Number of Students} \]
\[ \text{Total Height} = 142 \, \text{cm} \times 16 \]
\[ \text{Total Height} = 2272 \, \text{cm} \]

### Step 2: Set up the equation for the new average height including the teacher.
When the teacher's height is included, the average height increases by 1 cm, making it 143 cm.

Now, the total number of individuals (students + teacher) is 17. Therefore, the new total height can be expressed as:
\[ \text{New Total Height} = \text{Total Height of Students} + \text{Height of Teacher} \]
Let the height of the teacher be \( x \). Thus, we can write:
\[ \text{New Total Height} = 2272 \, \text{cm} + x \]

### Step 3: Write the equation for the new average height.
The new average height is given by:
\[ \text{New Average Height} = \frac{\text{New Total Height}}{\text{Total Number of Individuals}} \]
Substituting the known values:
\[ 143 = \frac{2272 + x}{17} \]

### Step 4: Solve for the height of the teacher.
To eliminate the fraction, multiply both sides by 17:
\[ 143 \times 17 = 2272 + x \]
Calculating \( 143 \times 17 \):
\[ 2431 = 2272 + x \]
Now, isolate \( x \):
\[ x = 2431 - 2272 \]
\[ x = 159 \, \text{cm} \]

### Conclusion
The height of the teacher is **159 cm**.

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