Introduction

Math puzzles often serve as a fun and effective way to enhance problem-solving skills and logical thinking. One such puzzle involves the ages of two brothers, where their combined age is given, and the difference in their ages is known. In this article, we'll explore how to solve the puzzle, providing a step-by-step approach to help you arrive at the solution. This method will help you understand the underlying algebraic principles and apply them to similar problems in the future.

Solving the Age Puzzle

The puzzle states that the sum of the current ages of two brothers is 32. Additionally, the elder brother is 6 years older than the younger brother. How can we determine the ages of the two brothers?

Method 1:

Let's start by using a simple method to solve the puzzle. First, we need to subtract the age difference from the total age:

32 – 6 26

Now, divide this result by 2 to find the age of the younger brother:

26 ÷ 2 13

To find the age of the elder brother, add the age difference to the younger brother's age:

13 6 19

Thus, the younger brother is 13 years old, and the elder brother is 19 years old.

Using Algebraic Equations

Alternatively, we can use algebra to solve the puzzle. Let’s denote the age of the younger brother as x. The elder brother’s age would then be x 6. According to the problem, the sum of their ages is 32:

x (x 6) 32

Simplify the equation:

2x 6 32

Subtract 6 from both sides of the equation:

2x 26

Divide both sides by 2 to solve for x:

x 13

Now, add the age difference to find the elder brother's age:

13 6 19

As a result, the younger brother is 13 years old, and the elder brother is 19 years old.

Verification

To verify our solution, we can add the ages of the two brothers together:

13 19 32

This confirms that the sum of their ages is indeed 32, and the age difference between them is 6 years.

Conclusion

Solving age puzzles like this one can be an enjoyable way to practice algebraic concepts and strengthen your problem-solving abilities. By using both intuitive and algebraic methods, you can arrive at the correct solution and deepen your understanding of mathematical principles.

By the end, you will not only have found the ages of the two brothers but also developed a greater appreciation for the power of algebra in solving real-world problems.