If 37 a + 37 b =5661 , what is the average of a and b ?

Options

A. `74 . 5`
B. `151`
C. `76.5`
D. 153

Answer

To solve the question "If 37a + 37b = 5661, what is the average of a and b?", we can follow these steps:

### Step 1: Simplify the Equation
We start with the equation given:
\[ 37a + 37b = 5661 \]

### Step 2: Factor Out the Common Term
Notice that both terms on the left side have a common factor of 37. We can factor this out:
\[ 37(a + b) = 5661 \]

### Step 3: Divide Both Sides by 37
To isolate \( a + b \), we divide both sides of the equation by 37:
\[ a + b = \frac{5661}{37} \]

### Step 4: Calculate the Value of \( a + b \)
Now, we perform the division:
\[ a + b = 153 \]

### Step 5: Find the Average of \( a \) and \( b \)
The average of two numbers \( a \) and \( b \) is given by the formula:
\[ \text{Average} = \frac{a + b}{2} \]
Substituting the value we found:
\[ \text{Average} = \frac{153}{2} \]

### Step 6: Perform the Division
Now, we calculate:
\[ \text{Average} = 76.5 \]

### Final Answer
Thus, the average of \( a \) and \( b \) is:
\[ \text{Average} = 76.5 \]

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