The Riddle of Ages: A Mathematical Puzzle and Its Solution

The mathematical puzzle of ages can be quite intriguing, especially when it involves familial relationships. In this article, we'll explore the solution to the riddle: 'When my son was 13 years old, I was just 33 years old. Now my age is twice as old as his age. What is my present age?' This problem involves basic algebra and logic, making it an excellent exercise for anyone interested in problem-solving.

Understanding the Problem

The problem can be broken down into two parts. First, we know that five years ago, the father was five times as old as his son. Second, the father's current age is three times the son's current age. Let's denote the father's age by F and the son's age by S.

Step 1: Setting Up the Equations

Mathematically, the given conditions can be written as the following two equations:

The first condition: Five years ago, the father was five times as old as his son. The second condition: Currently, the father's age is three times the son's age.

These conditions can be expressed as:

[ F - 5 5(S - 5) ] [ F 3S ]

Step 2: Solving the Equations

To solve the equations, we start by substituting the second equation into the first:

[ 3S - 5 5(S - 5) ]

Cleaning this up, we get:

[ 3S - 5 5S - 25 ]

Next, we group the terms involving S:

[ 5S - 3S 25 - 5 ]

This simplifies to:

[ 2S 20 ]

Solving for S:

[ S 10 ]

Now, using the second equation:

[ F 3S ]

Substituting S 10 into this equation:

[ F 3 times 10 ]

So, the father's age is:

[ F 30 ]

Conclusion

The problem states that the father is currently 30 years old and the son is 10 years old, making the father's age 30 years old. This conclusion aligns with the given conditions in the problem.

Alternative Solutions and Logic

Another approach involves simple logic. Starting from the given ages of the son and the mother, we can deduce the age needed for the mother's age to be double the son's age.

13 - 33 14 - 34 15 - 35 16 - 36 17 - 37 18 - 38 19 - 39 20 - 40

Here, we see that at 20 years of age, the mother is 40 years old, which is twice the son's age. Thus, the son's current age is 20 and the mother's current age is 40.

Conclusion

The son is 20 years old, and the mother is 40 years old, making the mother's age double the son's age. This logical approach confirms the consistency of the solution.

Conclusion and Further Exploration

This problem not only tests one's ability in algebraic problem-solving but also sharpens logical reasoning skills. It's a great example of how mathematics and logic can be intertwined in real-world problems.

Key Takeaways

The solution to the age puzzle involves setting up and solving equations. Logical reasoning helps validate the solution. The problem demonstrates the importance of understanding the relationship between variables.

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