Solving for the Third Integer in a Sum Problem

Understanding and solving integer problems is a fundamental skill in mathematics that can simplify complex problems. This article will guide you through solving a specific problem using simple algebraic techniques. Letrsquo;s dive in!

Problem Statement

Given three integers, the sum of which is 65. Two of the integers are -31 and 14. We need to find the third integer.

Step-by-Step Solution

Letrsquo;s denote the third integer as x. Our problem can be represented as an equation:

x - 31 14 65

This equation can be simplified as follows:

x - 17 65

To isolate x, we need to get rid of -17 on the left side. We do this by adding 17 to both sides of the equation:

x - 17 17 65 17

This simplifies to:

x 82

Therefore, the third integer is 82.

Another Approach

Let us assume the unknown integer is X. The equation can be written as follows:

X - 31 14 65

Combine the constants on the left side:

X - 17 65

Add 17 to both sides:

X 65 17

Therefore, we get:

X 82

The third integer is 82.

Understanding Algebraic Techniques

Algebraic techniques are essential for solving such problems. Understanding how to isolate variables is crucial. By following the steps above, we can solve for any unknown value in the equation by ensuring the equation remains balanced. This method is not only systematic but also easier to apply as the complexity of the equations increases.

Practical Application

This problem-solving approach can be applied in various real-world scenarios. For instance, when dealing with financial transactions, you might need to account for all debits and credits to ensure the total is accurate. Similarly, in inventory management, ensuring that the sum of all items is consistent helps in maintaining accurate records.

Conclusion

Understanding and solving integer problems is a foundational skill in mathematics that extends beyond the classroom. By mastering algebraic techniques, you can solve a wide range of problems efficiently. In the next section, we will explore some common pitfalls and tips to avoid them.