Average of 5 consecutive number is 23. Find the largest number

Answer

To solve the problem of finding the largest number among five consecutive numbers whose average is 23, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Consecutive Numbers**:
Let the first of the five consecutive numbers be represented as \( x \). Therefore, the five consecutive numbers can be expressed as:
- First number: \( x \)
- Second number: \( x + 1 \)
- Third number: \( x + 2 \)
- Fourth number: \( x + 3 \)
- Fifth number: \( x + 4 \)

2. **Calculate the Average**:
The average of these five numbers is given by the formula:
\[ \text{Average} = \frac{\text{Sum of the numbers}}{\text{Total numbers}} \]
The sum of the five numbers is:
\[ x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 5x + 10 \]
Therefore, the average can be written as:
\[ \text{Average} = \frac{5x + 10}{5} = x + 2 \]

3. **Set Up the Equation**:
According to the problem, the average is 23. Thus, we can set up the equation:
\[ x + 2 = 23 \]

4. **Solve for \( x \)**:
To find \( x \), we subtract 2 from both sides of the equation:
\[ x = 23 - 2 = 21 \]

5. **Find the Largest Number**:
The largest of the five consecutive numbers is:
\[ x + 4 = 21 + 4 = 25 \]

### Final Answer:
The largest number among the five consecutive numbers is **25**.

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