Solving the Equation: Two Fifths of a Number is 24

Mathematics often involves solving problems with equations. One such problem is determining a number when you know that two-fifths of it equals 24. Let's explore the steps to solve this equation and how to use algebra to find the unknown value.

Understanding the Problem

The problem states that two-fifths of a number is 24. We can represent this as:

2/5 of X 24

Solving the Equation

To solve this equation, we need to find the value of X. Here are the steps to solve for X:

Start with the given equation: 2/5 * X 24 To isolate X, we need to multiply both sides of the equation by the reciprocal of 2/5, which is 5/2: X 24 * (5/2) Now, perform the multiplication: X 24 * 2.5 60

Verification

To ensure our solution is correct, we can substitute X 60 back into the original equation:

2/5 * 60 24

2/5 * 60 (2 * 60) / 5 120 / 5 24

The equation holds true, confirming that 60 is indeed the correct solution.

Alternative Methods

There are other ways to solve this problem, and some may turn to the Internet for guidance. Here are a few alternative approaches:

Solving by Direct Multiplication: Since you know that half of a number is 24, you can multiply 24 by 5/2, which is the same as multiplying by 2.5. Using Algebra: Express the problem as X/2 24 and then multiply both sides by 2 to solve for X. Using Proportions: Set up a proportion where 2 parts is to 5 parts as 24 is to the unknown number X, and solve for X.

Conclusion

Understanding and solving equations like "two-fifths of a number is 24" is a fundamental skill in algebra. Whether you use multiplication, algebraic manipulation, or a direct approach, the solution remains consistent. By following these steps, you can confidently solve such problems and tackle more complex algebraic equations in the future.

Frequently Asked Questions (FAQs)

Q: How do you solve problems like 'two-fifths of a number is 24'?
rA: First, set up the equation (2/5 * X 24). Then, isolate X by multiplying both sides by 5/2, resulting in X 60.

Q: What are some common methods for solving algebraic equations?
rA: Common methods include direct multiplication, algebraic manipulation, and using proportions.

Q: Why is it important to understand solving algebraic equations?
rA: Understanding these concepts helps in various fields, including science, engineering, and finance, where algebraic models are used to solve real-world problems.