If the sum of three consecutive integers is 21, then the sum of the two smaller integers is :

Options

A. 11
B. 5
C. 12
D. 13

Answer

To solve the problem of finding the sum of the two smaller integers when the sum of three consecutive integers is 21, follow these steps:

### Step 1: Define the integers
Let the three consecutive integers be represented as:
- First integer: \( x \)
- Second integer: \( x + 1 \)
- Third integer: \( x + 2 \)

### Step 2: Set up the equation
According to the problem, the sum of these three consecutive integers is 21. Therefore, we can write the equation:
\[ x + (x + 1) + (x + 2) = 21 \]

### Step 3: Simplify the equation
Combine like terms:
\[ 3x + 3 = 21 \]

### Step 4: Solve for \( x \)
Subtract 3 from both sides:
\[ 3x = 21 - 3 \]
\[ 3x = 18 \]
Now, divide both sides by 3:
\[ x = 6 \]

### Step 5: Identify the integers
Now that we have \( x \), we can find the three consecutive integers:
- First integer: \( 6 \)
- Second integer: \( 7 \)
- Third integer: \( 8 \)

### Step 6: Find the sum of the two smaller integers
Now, we need to find the sum of the two smaller integers:
\[ 6 + 7 = 13 \]

### Final Answer
The sum of the two smaller integers is \( 13 \).

---