If 47a + 47b = 5452, what is the average of a and b?

Options

A. 116
B. 23.5
C. 96
D. 58

Answer

To solve the problem, we need to find the average of \( a \) and \( b \) given the equation \( 47a + 47b = 5452 \).

### Step-by-Step Solution:

1. **Start with the given equation:**
\[ 47a + 47b = 5452 \]

2. **Factor out the common term (47):**
\[ 47(a + b) = 5452 \]

3. **Divide both sides by 47 to isolate \( a + b \):**
\[ a + b = \frac{5452}{47} \]

4. **Calculate \( \frac{5452}{47} \):**
\[ a + b = 116 \]

5. **Now, to find the average of \( a \) and \( b \), use the formula for average:**
\[ \text{Average} = \frac{a + b}{2} \]

6. **Substitute \( a + b \) into the average formula:**
\[ \text{Average} = \frac{116}{2} \]

7. **Calculate the average:**
\[ \text{Average} = 58 \]

### Final Answer:
The average of \( a \) and \( b \) is \( 58 \).

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