The mean of a, b, c, d and e is 36. If the mean of b, d and e is 32, what is the mean of a and c?

Options

A. 24
B. 44
C. 42
D. 46

Answer

To solve the problem step by step, we can follow these calculations:

1. **Understanding the Mean of A, B, C, D, and E**:
- We know that the mean of \( a, b, c, d, e \) is 36.
- The formula for mean is given by:
\[ \text{Mean} = \frac{\text{Sum of values}}{\text{Number of values}} \]
- Therefore, we can write:
\[ \frac{a + b + c + d + e}{5} = 36 \]
- Multiplying both sides by 5 gives:
\[ a + b + c + d + e = 180 \quad \text{(1)} \]

2. **Understanding the Mean of B, D, and E**:
- We also know that the mean of \( b, d, e \) is 32.
- Using the same formula for mean:
\[ \frac{b + d + e}{3} = 32 \]
- Multiplying both sides by 3 gives:
\[ b + d + e = 96 \quad \text{(2)} \]

3. **Finding the Sum of A and C**:
- We need to find the sum of \( a \) and \( c \).
- We can do this by subtracting equation (2) from equation (1):
\[ (a + b + c + d + e) - (b + d + e) = 180 - 96 \]
- This simplifies to:
\[ a + c = 84 \quad \text{(3)} \]

4. **Calculating the Mean of A and C**:
- Now that we have the sum of \( a \) and \( c \), we can find their mean:
\[ \text{Mean of } a \text{ and } c = \frac{a + c}{2} = \frac{84}{2} = 42 \]

Thus, the mean of \( a \) and \( c \) is **42**.