Subtracting 3 from Both Sides

Oct 13, 2025 by miodeya.com 42 views

Introduction

In this article, we will delve into a mathematical puzzle that involves a father and his son. The problem states that Alex is 9 times the age of his son, and in 3 years, he will be 5 times the age of his son. Our goal is to determine their current ages.

Let's Break Down the Problem

To solve this problem, we need to use algebraic equations. Let's denote the current age of Alex as A and the current age of his son as S.

From the first statement, we know that Alex is 9 times the age of his son. This can be represented as:

A = 9S

The Second Statement: A Future Equation

In 3 years, Alex will be A + 3 years old, and his son will be S + 3 years old. According to the second statement, in 3 years, Alex will be 5 times the age of his son. This can be represented as:

A + 3 = 5(S + 3)

Simplifying the Equation

Now, let's simplify the second equation by expanding the parentheses:

A + 3 = 5S + 15

Subtracting 3 from Both Sides

To isolate the variable A, we need to subtract 3 from both sides of the equation:

A = 5S + 15 - 3

A = 5S + 12

Substituting the First Equation

Now, we can substitute the first equation (A = 9S) into the simplified second equation:

9S = 5S + 12

Subtracting 5S from Both Sides

To isolate the variable S, we need to subtract 5S from both sides of the equation:

4S = 12

Dividing Both Sides by 4

Now, we can divide both sides of the equation by 4 to solve for S:

S = 12/4

S = 3

Finding Alex's Age

Now that we know the son's age (S = 3), we can find Alex's age by substituting S into the first equation (A = 9S):

A = 9(3)

A = 27

Conclusion

In conclusion, Alex is currently 27 years old, and his son is currently 3 years old.

What's Next?

In the next section, we will explore more mathematical puzzles and problems. Stay tuned for more exciting math challenges!

Additional Resources

If you want to learn more about algebraic equations and how to solve them, here are some additional resources:

Khan Academy: Algebra
Mathway: Algebra Solver
Wolfram Alpha: Algebra Calculator

Final Thoughts

Solving mathematical puzzles like this one requires patience, persistence, and practice. With these skills, you can tackle even the most challenging math problems. Keep practicing, and you'll become a math master in no time!

Mathematical Puzzle Solutions

Solving the Mystery of the Missing Numbers
The Mysterious Case of the Missing Digit
The Enigma of the Missing Pattern

Mathematical Puzzle Resources

Khan Academy: Algebra
Mathway: Algebra Solver
Wolfram Alpha: Algebra Calculator
Frequently Asked Questions (FAQs) About the Alex and His Son's Ages Problem ================================================================================

Introduction

In our previous article, we solved the mystery of Alex and his son's ages. However, we received many questions from readers who wanted to know more about the problem. In this article, we will answer some of the most frequently asked questions (FAQs) about the problem.

Q: What is the main concept behind the problem?

A: The main concept behind the problem is the use of algebraic equations to solve a real-world problem. We used two equations to represent the relationship between Alex's age and his son's age.

Q: Why did we use two equations?

A: We used two equations because we had two pieces of information: Alex is 9 times the age of his son, and in 3 years, he will be 5 times the age of his son. Each equation represented one of these pieces of information.

Q: How did we simplify the second equation?

A: We simplified the second equation by expanding the parentheses and then subtracting 3 from both sides. This helped us isolate the variable A.

Q: Why did we substitute the first equation into the simplified second equation?

A: We substituted the first equation into the simplified second equation because it allowed us to eliminate the variable A and solve for the variable S.

Q: What is the significance of the variable S?

A: The variable S represents the current age of Alex's son. By solving for S, we were able to determine the current age of Alex's son.

Q: How did we find Alex's age?

A: We found Alex's age by substituting the value of S into the first equation (A = 9S). This allowed us to determine the current age of Alex.

Q: What is the relationship between the two equations?

A: The two equations are related because they represent the same real-world problem. The first equation represents the current relationship between Alex's age and his son's age, while the second equation represents the future relationship between their ages.

Q: Can we use this method to solve other problems?

A: Yes, we can use this method to solve other problems that involve algebraic equations. The key is to identify the variables and the relationships between them, and then use algebraic techniques to solve for the variables.

Q: What are some common mistakes to avoid when solving algebraic equations?

A: Some common mistakes to avoid when solving algebraic equations include:

Not reading the problem carefully and understanding what is being asked
Not identifying the variables and the relationships between them
Not using the correct algebraic techniques to solve for the variables
Not checking the solution to make sure it makes sense in the context of the problem

Conclusion

In conclusion, the Alex and his son's ages problem is a classic example of how algebraic equations can be used to solve real-world problems. By understanding the concepts and techniques involved, we can use this method to solve other problems and become more confident in our ability to solve algebraic equations.

Additional Resources

If you want to learn more about algebraic equations and how to solve them, here are some additional resources:

Khan Academy: Algebra
Mathway: Algebra Solver
Wolfram Alpha: Algebra Calculator

Final Thoughts

Solving algebraic equations is an important skill that can be used in a wide range of applications, from science and engineering to finance and economics. By practicing and becoming more confident in our ability to solve algebraic equations, we can become more effective problem-solvers and achieve our goals.

Mathematical Puzzle Solutions

Solving the Mystery of the Missing Numbers
The Mysterious Case of the Missing Digit
The Enigma of the Missing Pattern