Solving a Math Puzzle: Calculating Future Ages Based on Age Ratios

Introduction

Math puzzles often revolve around logical reasoning and algebraic equations. In this article, we will walk through a typical math problem where we need to determine the future ages of individuals based on given age ratios. The specific problem involves three individuals: A, B, and C. We will break down the steps and use algebra to find the solution.

Understanding the Problem

The problem statement provides us with the following information:

B's age is 6 years older than A. The ratio of B's age 9 years hence to C's present age is 9:8. C's present age is twice A's age. We need to find B's age after 5 years.

Step-by-Step Solution

Let's denote the current age of A as x.

Determining the Ages

B's age is 6 years older than A.

So, if A's age is x, B's age is x 6.

C's present age is twice A's age.

So, C's age is 2x.

The ratio of B's age 9 years hence to C's present age is 9:8.

9 Years hence, B's age will be (x 6) 9 x 15.

The given ratio is (x 15) : 2x 9 : 8.

Using algebra:

8(x 15) 9(2x)

Expanding and simplifying:

8x 120 18x

120 18x - 8x

120 1

x 12

Now, we can calculate the present ages:

A's current age is x 12. B's current age is x 6 18. C's current age is 2x 24.

Data After 5 Years

After 5 years:

A's age will be 12 5 17 years. B's age will be 18 5 23 years. C's age will be 24 5 29 years.

Conclusion

From the algebraic solution, we determined that B’s current age is 18 years. Therefore, B's age after 5 years will be 23 years.

Additional Resources

For more detailed solutions and methods, you can watch the following video:

Video Tutorial: Solving Age Ratio Problems

Keywords: age ratios, algebraic equations, future ages, mathematical puzzles