The sum of five numbers A, B, C, D and E is 37.5. The average of A and B is 6, and the average of D and E is 9. The average of A, B and C is:

Options

A. `7.5`
B. 6
C. `6.5`
D. `5.5`

Answer

To solve the problem step by step, we will break down the information given and calculate the required average.

### Step 1: Understand the given information
We know:
1. The sum of five numbers \( A, B, C, D, \) and \( E \) is \( 37.5 \).
2. The average of \( A \) and \( B \) is \( 6 \).
3. The average of \( D \) and \( E \) is \( 9 \).

### Step 2: Calculate the sum of \( A \) and \( B \)
The average of \( A \) and \( B \) is given by:
\[ \text{Average} = \frac{A + B}{2} = 6 \]
Multiplying both sides by \( 2 \):
\[ A + B = 6 \times 2 = 12 \]

### Step 3: Calculate the sum of \( D \) and \( E \)
The average of \( D \) and \( E \) is given by:
\[ \text{Average} = \frac{D + E}{2} = 9 \]
Multiplying both sides by \( 2 \):
\[ D + E = 9 \times 2 = 18 \]

### Step 4: Find the value of \( C \)
Now, we know:
\[ A + B + C + D + E = 37.5 \]
Substituting the values we found for \( A + B \) and \( D + E \):
\[ 12 + C + 18 = 37.5 \]
Combining the constants:
\[ C + 30 = 37.5 \]
To find \( C \), subtract \( 30 \) from both sides:
\[ C = 37.5 - 30 = 7.5 \]

### Step 5: Calculate the average of \( A, B, \) and \( C \)
Now we can find the average of \( A, B, \) and \( C \):
\[ \text{Average of } A, B, C = \frac{A + B + C}{3} \]
Substituting the known values:
\[ \text{Average of } A, B, C = \frac{12 + 7.5}{3} = \frac{19.5}{3} = 6.5 \]

### Final Answer
The average of \( A, B, \) and \( C \) is \( 6.5 \).

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