The average of a,b, and c is 79 and the average of a and c is also 79.then the value of b is:

Options

A. 0
B. 79
C. -79
D. none of these

Answer

To find the value of \( b \), we can follow these steps:

1. **Understand the given averages**:
- The average of \( a, b, c \) is 79.
- The average of \( a, c \) is also 79.

2. **Set up the equations**:
- The average of \( a, b, c \) can be expressed as:
\[ \frac{a + b + c}{3} = 79 \]
- Multiplying both sides by 3 gives:
\[ a + b + c = 79 \times 3 = 237 \quad \text{(Equation 1)} \]

- The average of \( a, c \) can be expressed as:
\[ \frac{a + c}{2} = 79 \]
- Multiplying both sides by 2 gives:
\[ a + c = 79 \times 2 = 158 \quad \text{(Equation 2)} \]

3. **Substitute Equation 2 into Equation 1**:
- From Equation 1, we have:
\[ a + b + c = 237 \]
- From Equation 2, we know:
\[ a + c = 158 \]
- We can substitute \( a + c \) from Equation 2 into Equation 1:
\[ 158 + b = 237 \]

4. **Solve for \( b \)**:
- Rearranging the equation gives:
\[ b = 237 - 158 \]
- Calculating the right side:
\[ b = 79 \]

Thus, the value of \( b \) is \( 79 \).