This problem requires finding the smallest of four consecutive even numbers whose sum is 484.

Numbers Representation

Let the smallest even number be represented by the variable $x$. Since the numbers are consecutive even numbers, they increase by 2 each time. Therefore, the four consecutive even numbers can be represented as:

• First number: \( x \)
• Second number: \( x + 2 \)
• Third number: \( x + 4 \)
• Fourth number: \( x + 6 \)

Sum Equation Formulation

The problem states that the sum of these four numbers is 484. We can set up an equation:

\( x + (x + 2) + (x + 4) + (x + 6) = 484 \)

Solving for Smallest Number

Now, simplify and solve the equation for $x$:

1. Combine like terms: \( (x + x + x + x) + (2 + 4 + 6) = 484 \)
2. This simplifies to: \( 4x + 12 = 484 \)
3. Subtract 12 from both sides of the equation: \( 4x = 484 - 12 \)
4. \( 4x = 472 \)
5. Divide both sides by 4 to find the value of \( x \): \( x = \frac{472}{4} \)
6. \( x = 118 \)

The variable $x$ represents the smallest of the four consecutive even numbers.

Smallest Number Identified

The value calculated for \( x \) is 118. This is the smallest number among the four consecutive even numbers.

The four numbers are 118, 120, 122, and 124. Their sum is \( 118 + 120 + 122 + 124 = 484 \), confirming the result.