Calculating Age with Mathematical Puzzles: How Old Am I When My Brother Is 50?

Have you ever come across a challenge that requires you to think about the passage of time and the relationships between ages? Let’s explore a common puzzle that boggles the mind:

Introduction to the Puzzle

When you were 10, your brother was half your age. Now that your brother is 50, how old are you?

Solving the Puzzle Step-by-Step

1. Understanding the Initial Condition: When you were 10, your brother was half your age. Therefore, your brother was 5 years old at that time. 2. Identifying the Age Difference: The age difference between you and your brother is 5 years. This difference remains constant over time.

Calculating Your Current Age

1. Current Age of Your Brother: If your brother is now 50, and the age difference between you and your brother is 5 years, then you are 5 years younger than him. 2. Mathematical Calculation: Your age Your brother's age - 5

Applying the formula:

[ text{Your age} 50 - 5 45 ]

However, this is not the correct answer because we need to solve it differently. We should recognize that even though your brother has aged 45 years (50 - 5 45), your age must be the original age difference of 10 years added to his current age.

Revising the Calculation

1. Correct Approach: Since your brother is 50 and the difference between your ages is 5 years, your age should be the total age of your brother plus your original age difference. 2. Mathematical Calculation: Your age 50 (10 - 5) 50 5 55

Therefore, you are 55 years old now.

Additional Insight: The 5/6ths Rule

Another perplexing way to solve this problem is to use the 5/6ths rule. If your brother is now 5/6ths of your age, you can set up the equation:

[ frac{5}{6} times text{Your age} 50 ]

Solving for your age:

[ text{Your age} 50 times frac{6}{5} 60 / 5 times 6 6 times 10 55 ]

Thus, you are 55 years old.

Conclusion

Now that we’ve walked through this problem, it’s clear that the key to solving it lies in understanding the constant age difference and applying simple algebra. Whether you use the straightforward method or the 5/6ths rule, the result is the same: you are 55 years old.

These types of puzzles not only test our mathematical abilities but also our ability to think critically and logically.