There are three positive numbers. If the average of any two of them is added to the third number, the resulting sums are 154. 148 and 132. The average of the original three numbers is:

Options

A. `75 1/3`
B. `72 1/3`
C. `70 1/3`
D. `76 1/3`

Answer

To solve the problem, we need to find the average of three positive numbers \( A \), \( B \), and \( C \) given that the average of any two of them added to the third number results in specific sums.

### Step-by-step Solution:

1. **Set Up the Equations**:
- The average of \( A \) and \( B \) added to \( C \) gives us:
\[ \frac{A + B}{2} + C = 154 \]
Multiplying through by 2:
\[ A + B + 2C = 308 \quad \text{(Equation 1)} \]

- The average of \( B \) and \( C \) added to \( A \) gives us:
\[ \frac{B + C}{2} + A = 148 \]
Multiplying through by 2:
\[ B + C + 2A = 296 \quad \text{(Equation 2)} \]

- The average of \( A \) and \( C \) added to \( B \) gives us:
\[ \frac{A + C}{2} + B = 132 \]
Multiplying through by 2:
\[ A + C + 2B = 264 \quad \text{(Equation 3)} \]

2. **Add the Equations**:
- Now we add all three equations together:
\[ (A + B + 2C) + (B + C + 2A) + (A + C + 2B) = 308 + 296 + 264 \]
- This simplifies to:
\[ 4A + 4B + 4C = 868 \]

3. **Simplify the Equation**:
- Dividing the entire equation by 4:
\[ A + B + C = 217 \]

4. **Calculate the Average**:
- The average of the three numbers \( A \), \( B \), and \( C \) is:
\[ \text{Average} = \frac{A + B + C}{3} = \frac{217}{3} = 72.33 \]

### Final Answer:
The average of the original three numbers is approximately \( 72.33 \).