Solving for Four Consecutive Numbers Whose Sum is 402

Introduction

In algebra, solving for a set of consecutive numbers whose sum meets a specific condition is a common problem. This article demonstrates how to find four consecutive numbers that add up to 402, using both a detailed step-by-step approach and a more concise solution. This content is optimized for Google search algorithms, providing a clear, educational, and SEO-friendly format.

Problem Statement

The problem statement is to find four consecutive numbers such that their sum equals 402. Four consecutive numbers can be represented as x, x 1, x 2, and x 3. The sum of these four numbers is given as:

Step-by-Step Solution

The sum of the four consecutive numbers can be expressed as:

x (x 1) (x 2) (x 3) 402

Let's simplify the equation:

4x 6 402

Now, let's subtract 6 from both sides of the equation:

4x 396

Dividing both sides by 4:

x 99

Thus, the four consecutive numbers are:

Therefore, the four consecutive numbers are 99, 100, 101, and 102.

Concise Solution

If you prefer a succinct approach, you can set up the equation as follows:

x (x 1) (x 2) (x 3) 402

Simplify:

4x 6 402

Subtract 6 from both sides:

4x 396

Divide by 4:

x 99

Therefore, the four consecutive numbers are:

Conclusion

To summarize, when faced with the problem of finding four consecutive numbers that add up to 402, the solution involves setting up an algebraic equation and solving it systematically. The four consecutive numbers that satisfy the given condition are 99, 100, 101, and 102. This method can be applied to similar problems involving consecutive numbers and their sums.

Further Reading

For more in-depth understanding and additional practice, consider exploring articles on solving algebraic equations, consecutive numbers, and other mathematical concepts.