Math Puzzles and Solutions: How to Calculate the Combined Age of Four Brothers Over Time

Mathematics can be both fun and challenging, especially when dealing with word problems that involve age calculations. In this article, we will explore a series of interesting math puzzles related to the ages of four brothers. We will solve these puzzles using algebraic equations and basic arithmetic to find the answers. Let's begin with the first problem.

Solving the First Problem

In the first scenario, we are given that in 15 years' time, the combined age of four brothers will be 107 years.

Solution:

Let us denote the current combined age of the brothers as x. In 15 years, each brother will be 15 years older, and since there are four brothers, the total increase in combined age over these 15 years is 60 years. Therefore, we can write the equation as:

x 60 107

To find the current combined age x, we rearrange the equation:

x 107 - 60 47

So, the current combined age of the four brothers is 47 years.

To find their combined age in six years, we calculate:

47 24 71

Hence, in six years' time, the combined age of the four brothers will be 71 years.

Solving the Second Problem

In the second scenario, we are given that in 20 years, the combined age of the four brothers will be 110 years.

Solution:

Let us denote the current combined age of the brothers as X. In 20 years, each brother will be 20 years older, and since there are four brothers, the total increase in combined age over these 20 years is 80 years. Therefore, we can write the equation as:

X 80 110

To find the current combined age X, we rearrange the equation:

X 110 - 80 30

So, the current combined age of the four brothers is 30 years.

To find their combined age in seven years, we calculate:

30 7 * 4 30 28 58

Hence, in seven years' time, the combined age of the four brothers will be 58 years.

A More General Approach

In the third scenario, we are asked to find the combined age of four brothers in seven years, given that in 20 years' time, the combined age will be 110 years.

Solution:

Let us denote the current combined age of the brothers as t. In 20 years, each brother will be 20 years older, and since there are four brothers, the total increase in combined age over these 20 years is 80 years. Therefore, we can write the equation as:

t 80 110

To find the current combined age t, we rearrange the equation:

t 110 - 80 30

So, the current combined age of the four brothers is 30 years.

To find their combined age in seven years, we calculate:

30 7 * 4 30 28 58

Hence, in seven years' time, the combined age of the four brothers will be 58 years.

Conclusion

Math puzzles like these can be fascinating and provide great practice in algebraic thinking and arithmetic skills. By breaking down the problems step-by-step, we can easily find the answers without needing to know the individual ages of the brothers. Whether you are a student, a teacher, or someone who just enjoys solving puzzles, these types of problems can be a fun brain teaser.

Key Takeaways:

Math puzzles involving age calculations can be solved using linear equations. By identifying the increase in age over a given period, we can find the current combined age. The combined age in the future can be calculated by adding the increase to the current combined age.

Keywords

math puzzle, combined age, age calculation