Finding the Answer: A Mathematical Puzzle About Ages

It's not uncommon for us to be faced with intriguing problems that test our reasoning and mathematical skills. The puzzle below, about a father and his son, is a classic example. Let's break it down step by step to find the solution.

The Problem

When your father was 33 years old, you were 5 years old. Now, your father is twice as old as you are. How old are you now?

Analysis of the Given Information

Here, we have two key pieces of information:

Your father was 33 years old when you were 5 years old. Currently, your father is twice as old as you.

Setting Up the Equation

Let's denote your current age as x. Since your father is twice as old as you, his current age would be 2x.

From the first piece of information, we know the age difference between you and your father is 28 years (33 - 5 28). This age difference remains constant over time, so we can write the equation:

x 28 2x

Solving the Equation

Now, let's solve for x to find your current age:

Start with the equation: x 28 2x Subtract x from both sides: 28 x

So, your current age is 28 years.

Verification

To verify, if you are 28 years old, then your father is 60 years old (28 28 60). This matches the condition that your father is twice as old as you.

Alternative Solutions and Analysis

Let's also consider the alternative solutions mentioned:

30 Years Old Solution

While one solution suggests you are 30, it is incorrect based on the given problem. This solution appears to misinterpret the age difference and does not account for the age being twice the difference.

35 Years Old Solution

The 35 years old solution does not fit the given data either, as it incorrectly applies the constant age difference without considering the twice-as-old condition.

Another Incorrect Solution

The 32, y 2y x 2, 32 y 4 2y, 32 y - 4 2y, 28 y 2y, 28 2y - y, 28 y, solution also misinterprets the relationship between the ages. It mistakenly sets up the equation without following the logical age differences and twice-as-old condition.

Conclusion

The correct age for you, based on the given puzzle, is 28 years. This solution logically follows from the provided information and ensures the father's age is twice that of the son.