To solve this problem, we need to determine the third number given the average of three numbers and the average of the first two numbers. Let's go through the steps systematically:
1. Find the total sum of the three numbers:
- The average of the three numbers is given as 8.
- Using the formula for average:
[tex]\[
\text{Average} = \frac{\text{Total sum of numbers}}{\text{Number of numbers}}
\][/tex]
- Therefore, the total sum of the three numbers is:
[tex]\[
\text{Total sum of three numbers} = \text{Average} \times \text{Number of numbers} = 8 \times 3 = 24
\][/tex]
2. Find the total sum of the first two numbers:
- The average of the first two numbers is given as 11.
- Using the same formula for average:
[tex]\[
\text{Total sum of the first two numbers} = \text{Average} \times \text{Number of numbers} = 11 \times 2 = 22
\][/tex]
3. Determine the third number:
- The third number is the difference between the total sum of the three numbers and the total sum of the first two numbers.
[tex]\[
\text{Third number} = \text{Total sum of three numbers} - \text{Total sum of the first two numbers} = 24 - 22 = 2
\][/tex]
Therefore, the third number is [tex]\( 2 \)[/tex].
The correct answer is B. 2.
