Solving Mathematical Problems: A Step-by-Step Guide

Mathematics is a fundamental tool for understanding the world around us. From basic arithmetic to complex algebraic equations, solving problems is a key skill in various fields. In this article, we will explore how to solve a specific mathematical problem step-by-step, providing a clear understanding of the logic and methods involved.

The Problem at Hand

A common type of mathematical problem involves finding the value of an unknown number based on given conditions. Consider the problem: When 12 is added to a certain number and the sum is multiplied by 4, the result is 60. Let's work through this step-by-step to explain how to solve it.

Step-by-Step Solution

To solve the problem, we can break it down into several steps:

Set up the equation: Represent the unknown number as ( x ). The equation can be written as: ( (x 12) times 4 60 ) Isolate the term with the unknown number: First, divide both sides of the equation by 4 to simplify: ( x 12 frac{60}{4} ) Calculate the right-hand side: ( x 12 15 ) Solve for the unknown number: Subtract 12 from both sides of the equation: ( x 15 - 12 ) Find the value of ( x ): ( x 3 )

Verification

To ensure the solution is correct, we can substitute ( x 3 ) back into the original equation and check if both sides are equal:

( (3 12) times 4 60 )

( 15 times 4 60 )

This confirms that the answer is indeed correct.

Alternative Methods

Another way to solve the problem is to first isolate the term involving the unknown number in the original equation. Here is an alternative approach:

Alternative Approach

Start with the original equation: ( x12 times 4 60 ) Divide both sides by 4: ( x12 frac{60}{4} ) Simplify the right-hand side: ( x12 15 ) Subtract 12 from both sides: ( x 15 - 12 ) Find the value of ( x ): ( x 3 )

Both methods lead to the same result, confirming the accuracy of the solution.

Conclusion

Solving mathematical problems requires a systematic approach and clear understanding. By breaking down the problem into smaller, manageable steps, we can arrive at a solution that is both correct and easy to verify. Whether you use the first method or the alternative approach, the goal is to isolate the unknown variable and solve for it step-by-step.

Further Exploration

For those interested in furthering their mathematical skills, exploring different types of algebraic equations and their solutions can be beneficial. Additionally, practicing a wide range of problems can help improve problem-solving abilities.

Related Keywords

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