The sum of three consecutive integers is 51. The middle one is :

Options

A. 14
B. 15
C. 16
D. 17

Answer

To solve the problem of finding the middle integer of three consecutive integers that sum to 51, we can follow these steps:

### Step 1: Define the integers
Let the three consecutive integers be represented as:
- First integer: \( x - 1 \)
- Second integer (middle one): \( x \)
- Third integer: \( x + 1 \)

### Step 2: Set up the equation
According to the problem, the sum of these three integers is equal to 51. Therefore, we can write the equation:
\[ (x - 1) + x + (x + 1) = 51 \]

### Step 3: Simplify the equation
Now, simplify the left side of the equation:
\[ x - 1 + x + x + 1 = 51 \]
This simplifies to:
\[ 3x = 51 \]

### Step 4: Solve for \( x \)
Now, divide both sides of the equation by 3 to find \( x \):
\[ x = \frac{51}{3} = 17 \]

### Step 5: Identify the middle integer
The middle integer, which we defined as \( x \), is:
\[ \text{Middle integer} = 17 \]

### Final Answer
The middle integer is **17**.

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