Finding the Present Age of the Father

Oct 13, 2025 by talynt.org 16 views

Introduction

Mathematical puzzles and problems are an essential part of mathematics education, helping students develop problem-solving skills and logical thinking. In this article, we will explore a mathematical puzzle involving a father and his son, where the father is four times as old as his son. We will also consider a scenario where five years ago, the son was one-seventh of the father's age. Our goal is to find the present age of the father, denoted as 'K'.

Understanding the Problem

Let's break down the problem into smaller, manageable parts. We are given two key pieces of information:

The father is four times as old as his son.
Five years ago, the son was one-seventh of the father's age.

We can represent the present age of the son as 'x'. Since the father is four times as old as his son, the present age of the father can be represented as '4x'.

Formulating the Equation

Now, let's consider the second piece of information: five years ago, the son was one-seventh of the father's age. We can represent the son's age five years ago as 'x - 5', and the father's age five years ago as '4x - 5'. According to the problem, the son's age five years ago was one-seventh of the father's age five years ago. We can set up an equation based on this information:

x - 5 = (1/7) × (4x - 5)

Solving the Equation

To solve the equation, we can start by multiplying both sides by 7 to eliminate the fraction:

7(x - 5) = 4x - 5

Expanding the left-hand side of the equation, we get:

7x - 35 = 4x - 5

Next, we can add 35 to both sides of the equation to get:

7x = 4x + 30

Subtracting 4x from both sides, we get:

3x = 30

Dividing both sides by 3, we get:

x = 10

Finding the Present Age of the Father

Now that we have found the present age of the son (x = 10), we can find the present age of the father, which is four times the son's age:

K = 4x = 4(10) = 40

Therefore, the present age of the father, denoted as 'K', is 40 years.

Conclusion

In this article, we explored a mathematical puzzle involving a father and his son, where the father is four times as old as his son. We also considered a scenario where five years ago, the son was one-seventh of the father's age. By formulating and solving an equation, we were able to find the present age of the father, which is 40 years. This problem requires a deep understanding of algebraic equations and problem-solving skills, making it an excellent example of a mathematical puzzle.

Frequently Asked Questions

Q: What is the present age of the son? A: The present age of the son is 10 years.
Q: What is the present age of the father? A: The present age of the father is 40 years.
Q: How old was the son five years ago? A: The son was 5 years old five years ago.
Q: How old was the father five years ago? A: The father was 35 years old five years ago.

Key Takeaways

The father is four times as old as his son.
Five years ago, the son was one-seventh of the father's age.
The present age of the son is 10 years.
The present age of the father is 40 years.
The son was 5 years old five years ago.
The father was 35 years old five years ago.

References

[1] Algebraic Equations
[2] Problem-Solving Skills
[3] Mathematical Puzzles

Note: The references provided are for general information purposes only and are not specific to this problem.

Introduction

In our previous article, we explored a mathematical puzzle involving a father and his son, where the father is four times as old as his son. We also considered a scenario where five years ago, the son was one-seventh of the father's age. By formulating and solving an equation, we were able to find the present age of the father, which is 40 years. In this article, we will provide a Q&A section to help clarify any doubts and provide additional information on the problem.

Q&A

Q: What is the present age of the son?

A: The present age of the son is 10 years.

Q: What is the present age of the father?

A: The present age of the father is 40 years.

Q: How old was the son five years ago?

A: The son was 5 years old five years ago.

Q: How old was the father five years ago?

A: The father was 35 years old five years ago.

Q: What is the relationship between the father's and son's ages?

A: The father is four times as old as his son.

Q: How did you find the present age of the father?

A: We formulated an equation based on the given information and solved it to find the present age of the father.

Q: What is the equation you used to find the present age of the father?

A: The equation is x - 5 = (1/7) × (4x - 5), where x is the present age of the son.

Q: Can you explain the steps you took to solve the equation?

A: Yes, we can break down the steps as follows:

Multiply both sides of the equation by 7 to eliminate the fraction.
Expand the left-hand side of the equation.
Add 35 to both sides of the equation.
Subtract 4x from both sides of the equation.
Divide both sides of the equation by 3.

Q: What is the significance of the number 7 in the equation?

A: The number 7 represents the fraction of the father's age that the son's age was five years ago.

Q: Can you provide more examples of mathematical puzzles like this one?

A: Yes, we can provide more examples of mathematical puzzles that involve algebraic equations and problem-solving skills.

Q: How can I improve my problem-solving skills?

A: To improve your problem-solving skills, you can practice solving mathematical puzzles and problems, and also try to identify patterns and relationships between different variables.

Conclusion

In this article, we provided a Q&A section to help clarify any doubts and provide additional information on the problem. We hope that this article has been helpful in understanding the mathematical puzzle involving a father and his son, and we encourage you to try solving more mathematical puzzles to improve your problem-solving skills.

Frequently Asked Questions

Q: What is the present age of the son? A: The present age of the son is 10 years.
Q: What is the present age of the father? A: The present age of the father is 40 years.
Q: How old was the son five years ago? A: The son was 5 years old five years ago.
Q: How old was the father five years ago? A: The father was 35 years old five years ago.

Key Takeaways

The father is four times as old as his son.
Five years ago, the son was one-seventh of the father's age.
The present age of the son is 10 years.
The present age of the father is 40 years.
The son was 5 years old five years ago.
The father was 35 years old five years ago.

References

[1] Algebraic Equations
[2] Problem-Solving Skills
[3] Mathematical Puzzles