The sum of two consecutive even number is 86. The large of the two is.

Options

A. `46`
B. `36`
C. `38`
D. `44`

Answer

To solve the problem of finding the larger of two consecutive even numbers whose sum is 86, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Variables**:
Let the first even number be represented as \( x \).

2. **Identify the Consecutive Even Number**:
The next consecutive even number can be expressed as \( x + 2 \).

3. **Set Up the Equation**:
According to the problem, the sum of these two consecutive even numbers is 86. Therefore, we can write the equation:
\[ x + (x + 2) = 86 \]

4. **Simplify the Equation**:
Combine like terms:
\[ 2x + 2 = 86 \]

5. **Isolate the Variable**:
Subtract 2 from both sides to simplify:
\[ 2x = 86 - 2 \]
\[ 2x = 84 \]

6. **Solve for \( x \)**:
Divide both sides by 2:
\[ x = \frac{84}{2} \]
\[ x = 42 \]

7. **Find the Larger Even Number**:
Now that we have \( x \), we can find the second even number:
\[ x + 2 = 42 + 2 = 44 \]

8. **Conclusion**:
The larger of the two consecutive even numbers is \( 44 \).

### Final Answer:
The larger of the two consecutive even numbers is **44**.

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