Solving Puzzles: When My Brother Was 12 I Was 1/2 His Age Plus 2

Introduction

Math puzzles can be a fun and challenging way to engage in logical thinking and enhance problem-solving skills. The classic problem of figuring out the age of individuals based on given relationships is a popular type of mathematical puzzle. In this article, we will explore the famous problem 'When my brother was 12, I was 1/2 his age plus 2. Now, he is 32. How old am I?' and delve into various methods to solve it.

Understanding the Puzzle

The statement 'When my brother was 12, I was 1/2 his age plus 2' provides the foundation for the puzzle. Here, the sibling relationship and the given age difference need to be exploited to find the current age of the speaker.

Methods to Solve the Puzzle

There are several methods to solve this puzzle, each offering a unique perspective. Let's explore a few of these methods:

Method 1: Direct Calculation

In this method, we begin by identifying the given information and applying simple arithmetic to find the solution.

Step 1: Determine the Speaker's Age When the Brother Was 12

When the brother was 12, the speaker was 1/2 of 12 2. This translates to:

1/2 * 12 2 6 2 8 years old.

Step 2: Calculate the Current Age Difference

Since the brother is now 32, and he was 12 when the speaker was 8, the difference in their ages is:

32 - 12 20 years.

Step 3: Calculate the Speaker's Current Age

Now, the speaker is 20 years older than her brother. Therefore, the current age of the speaker can be found by adding the age difference to the brother's current age:

32 20 - 20 25 5 (the 5-year age gap remains constant).

Conclusively, the speaker is 25 years old.

Method 2: Using Algebra

This approach uses algebraic equations to represent the given information and solve for the unknowns.

Step 1: Define Variables

Let y be the speaker's current age and b be the brother's current age.

Step 2: Set Up Equations

The first equation based on the statement 'When my brother was 12, I was 1/2 his age plus 2' is:

y - (12 - 10) 1/2 * 12 2

Which simplifies to:

y - 2 6 2 8

Solving for y gives:

y 8 2 10 20 (20 is the current age difference) 30 - 20 25 years.

Conclusion

The age calculation puzzle 'When my brother was 12, I was 1/2 his age plus 2. Now, he is 32. How old am I?' can be solved using various methods—direct calculation and algebraic equations. The correct answer is that the speaker is currently 25 years old. Such puzzles not only enhance logical reasoning but also provide a fun way to engage with mathematics.

Keywords: age calculation, mathematical puzzle, sibling age difference