Math Problem: When Will a Son Be Half His Father's Age?

Understanding the relationship between the ages of a father and his son can be approached through basic mathematical analysis. This article explores a specific question: at what point in time will the son's age be half of his father's age?

Introduction

Two individuals, a father and his son, have current ages of 30 years and 4 years, respectively. Our task is to determine in how many years, x, the son's age will be exactly half of his father's age.

Formulating the Equation

To solve this problem, we use algebra. Let us denote:

The current age of the father as F 30 years. The current age of the son as S 4 years. The number of years from now as x.

In x years, the father's age will be F x and the son's age will be S x. We need to find x such that:

S x (frac{1}{2}(emF xright))

Solving the Equation

Let's solve this step-by-step:

Multiply both sides by 2 to eliminate the fraction: (2 times (S x) 1 times (F x)) (2S 2x F x) Substitute the current ages of the father and son: (2 times 4 2x 30 x) (8 2x 30 x) Subtract x from both sides: (2x - x 30 - 8) (x 22)

Therefore, in 22 years, the son will be half the age of his father.

Verification

To verify this solution:

In 22 years, the father will be (30 22 52) years old. In 22 years, the son will be (4 22 26) years old.

Indeed, 26 is half of 52, confirming the accuracy of the solution.

Conclusion

The mathematical analysis shows how algebra can be used to solve real-life problems involving age relationships. It's worth noting that this solution is derived under idealized conditions, meaning it assumes steady aging without any interruptions or exceptions. The concept of age relationships is useful in many fields, including demography, actuarial science, and simple logical reasoning.