The average of five consecutive even numbers is 40. What is the smallest of these numbers?

Options

A. 24
B. 36
C. 35
D. 40

Answer

To find the smallest of five consecutive even numbers whose average is 40, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Average**: The average of a set of numbers is the sum of the numbers divided by the count of the numbers. Here, we have five consecutive even numbers.

2. **Set Up the Average Equation**: Given that the average of these five numbers is 40, we can express this mathematically as:
\[ \text{Average} = \frac{\text{Sum of the numbers}}{\text{Count of the numbers}} = 40 \]
Therefore, the sum of the five numbers can be calculated as:
\[ \text{Sum} = \text{Average} \times \text{Count} = 40 \times 5 = 200 \]

3. **Define the Consecutive Even Numbers**: Let the smallest of the five consecutive even numbers be \( x \). The five consecutive even numbers can then be represented as:
\[ x, \quad x+2, \quad x+4, \quad x+6, \quad x+8 \]

4. **Set Up the Sum Equation**: The sum of these five numbers can be expressed as:
\[ x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 200 \]
Simplifying this gives:
\[ 5x + (2 + 4 + 6 + 8) = 200 \]
\[ 5x + 20 = 200 \]

5. **Solve for \( x \)**: Now, we can isolate \( x \):
\[ 5x = 200 - 20 \]
\[ 5x = 180 \]
\[ x = \frac{180}{5} = 36 \]

6. **Conclusion**: The smallest of these five consecutive even numbers is \( x = 36 \).

### Final Answer:
The smallest of the five consecutive even numbers is **36**.