The average age of 20 students in a class is 15 yr. If the teacher's age is included, the average increases by one. What is the teacher's age?

Options

A. 30 yr
B. 21 yr
C. 42 yr
D. 36 yr

Explanation

To find the teacher's age based on the information provided, we can follow these steps:

### Step 1: Calculate the total age of the 20 students.
The average age of the 20 students is given as 15 years. To find the total age of the students, we multiply the average age by the number of students.

\[ \text{Total age of students} = \text{Average age} \times \text{Number of students} = 15 \times 20 = 300 \text{ years} \]

### Step 2: Determine the new average age when the teacher is included.
When the teacher's age is included, the average age increases to 16 years. Now we need to find the total age when the teacher is included.

\[ \text{Total age with teacher} = \text{New average age} \times \text{Total number of individuals} = 16 \times 21 = 336 \text{ years} \]

### Step 3: Set up the equation for the teacher's age.
Let the teacher's age be \( x \). The total age with the teacher can also be expressed as the total age of the students plus the teacher's age.

\[ \text{Total age with teacher} = \text{Total age of students} + \text{Teacher's age} \]
\[ 336 = 300 + x \]

### Step 4: Solve for the teacher's age.
Now we can solve for \( x \):

\[ x = 336 - 300 = 36 \text{ years} \]

### Conclusion:
The teacher's age is 36 years.

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