Solving the Problem: When a Certain Number is Added to 3 and the Result is Multiplied by 4 the Final Result is 60

Introduction to the Mathematical Problem

Mathematics often presents problems that require careful thought and the application of algebraic techniques. One such problem is determining an unknown number when the result of performing a series of operations on it is given. Let's explore this problem: When a certain number is added to 3 and the result is multiplied by 4, the final result is 60. What is the number?

Solving the Problem with Algebra

To solve this problem, let's denote the unknown number as x. According to the problem statement, the following sequence of operations is performed on x: Add 3 to the number: x 3 Multiply the result by 4: 4(x 3) Set the final result equal to 60: 4(x 3) 60

The equation that represents this situation is:

4x 12 60

Steps to Solve the Equation

To isolate the variable x, follow these steps:

Expand the expression on the left side of the equation: 4x 12 60 Subtract 12 from both sides of the equation to isolate the term with x: 4x 12 - 12 60 - 12 4x 48 Divide both sides of the equation by 4 to solve for x: 4x / 4 48 / 4 x 12

Verification of the Solution

To ensure that the solution is correct, substitute x 12 back into the original equation and verify: 4(12 3) 60

Performing the operations step by step:

Add 3 to 12: 12 3 15 Multiply the result by 4: 4 * 15 60

The final result is 60, which matches the given problem statement, confirming that our solution is correct.

Additional Insights and Applications

Understanding how to solve such algebraic equations not only enhances your problem-solving skills but also finds applications in various fields, including business, science, and engineering. For instance, in business, you might need to calculate break-even points, while in science, you could use similar techniques in physics to solve for unknown quantities in formulas.

Mathematics is not just about solving equations; it's about understanding the world around us through the language of numbers. As you practice more problems like these, you'll develop a deeper appreciation for the elegance and power of algebraic problem-solving.