Solving for Consecutive Even Numbers

Consecutive even numbers follow a pattern where each number is exactly two units apart. The task at hand is to determine the two consecutive even numbers that sum up to 94. To solve this problem, we need to set up an algebraic equation that reflects the given condition.

Setting Up the Equation

Let's denote the first even number as x. The next consecutive even number will then be x 2. The sum of these two numbers is given as 94. Therefore, we can write the equation as:

(x (x 2) 94)

Simplifying the equation, we get:

(2x 2 94)

Solving the Equation

To solve for x, we first subtract 2 from both sides of the equation:

(2x 92)

Next, we divide both sides by 2 to isolate x:

(x 46)

Thus, the first even number is 46. The next consecutive even number is 48.

Verification

Let's verify our solution by adding the two numbers together:

46 48 94

The solution is correct. The two consecutive even numbers are indeed 46 and 48.

Common Misconceptions

Sometimes, the wording of the problem might lead to confusion. For example, a similar problem might ask for a specific "number" rather than several numbers. In such cases, it's important to clarify with the context. For instance, if the problem had asked for the smaller number, the steps would be:

n (n 2) 94

The equation simplifies to:

2n 2 94

Subtracting 2 from both sides gives:

2n 92

Dividing both sides by 2, we get:

n 46

The smaller number is 46, and the larger number is 48.

Conclusion

Solving for consecutive even numbers involves setting up and solving an algebraic equation. The key is to clearly identify and define the variables. Understanding the underlying principles and the correct interpretation of the problem statement ensures accurate and reliable solutions.