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, we need to find three consecutive integers whose sum is 21 and then determine the sum of the two smaller integers.

### Step-by-Step Solution:

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

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

3. **Combine like terms**:
Simplifying the left side of the equation gives us:
\[ 3x + 3 = 21 \]

4. **Isolate the variable**:
To solve for \( x \), first subtract 3 from both sides:
\[ 3x = 21 - 3 \]
\[ 3x = 18 \]
Now, divide both sides by 3:
\[ x = \frac{18}{3} = 6 \]

5. **Find the three consecutive integers**:
Now that we have \( x = 6 \), the three consecutive integers are:
- First integer: \( 6 \)
- Second integer: \( 7 \)
- Third integer: \( 8 \)

6. **Calculate the sum of the two smaller integers**:
The two smaller integers are 6 and 7. Their sum is:
\[ 6 + 7 = 13 \]

### Final Answer:
The sum of the two smaller integers is **13**.