The sum of three consecutive numbers is 87. The middle number is

Options

A. 27
B. 29
C. 30
D. 28

Answer

To find the middle number of three consecutive integers whose sum is 87, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Consecutive Numbers**:
Let's denote the first consecutive number as \( x \). Therefore, the three consecutive numbers can be expressed as:
- First number: \( x \)
- Second number (middle number): \( x + 1 \)
- Third number: \( x + 2 \)

2. **Set Up the Equation**:
According to the problem, the sum of these three consecutive numbers is 87. We can write the equation:
\[ x + (x + 1) + (x + 2) = 87 \]

3. **Combine Like Terms**:
Simplifying the left side of the equation:
\[ x + x + 1 + x + 2 = 87 \]
This simplifies to:
\[ 3x + 3 = 87 \]

4. **Isolate the Variable**:
To solve for \( x \), first subtract 3 from both sides:
\[ 3x = 87 - 3 \]
This gives:
\[ 3x = 84 \]

5. **Solve for \( x \)**:
Now, divide both sides by 3:
\[ x = \frac{84}{3} \]
This simplifies to:
\[ x = 28 \]

6. **Find the Middle Number**:
The middle number is \( x + 1 \):
\[ x + 1 = 28 + 1 = 29 \]

### Final Answer:
The middle number is **29**.