Solving Age-related Brainteasers: A Man 30 Years Older Than His Son

Understanding and solving age-related problems can be a fun challenge, especially when they involve algebraic equations and simultaneous equations. One classic example is the problem where a man is 30 years older than his son, and in five years, his age will be twice the age of his son. Let's explore this problem and solve it step by step.

Problem Description

The problem can be stated as:

A man is 30 years older than his son. In 5 years, his age will be twice the age of his son. What is the present age of the father?

Step-by-Step Solution

Let's denote the present age of the son as S and the present age of the father as F.

We are given two pieces of information:

The father is 30 years older than his son:

F S 30

In 5 years, the father's age will be twice the son's age:

F 5 2(S 5)

Now we will substitute the first equation into the second equation to solve for S.

F 5 2(S 5)

Substituting F S 30 into the second equation:

S 30 5 2(S 5)

Let's simplify and solve for S:

S 35 2S 10

35 - 10 2S - S

25 S

So, the son's current age is 25 years. Now, we can find the father's age using the first equation:

F S 30 25 30 55

Therefore, the father's present age is 55 years.

Verification and Proof

To verify our solution, let's check if the father's age is twice the son's age in five years:

In 5 years:

The son's age will be 30:

S 5 25 5 30

The father's age will be 60:

F 5 55 5 60

Indeed, 60 2 times; 30, so our solution is correct.

Another Approach

Alternatively, let's consider another method to solve the problem:

If we denote the son's age as S, then the father's age can be expressed as:

The father is 30 years older than his son:

F 5S

In 5 years, the father's age will be twice the son's age:

F - 5 9S - 4

Substituting F 5S into the second equation:

5S - 5 9S - 4

Let's solve for S:

5S - 9S -4 5

-4S 1

S -1/4

However, this method seems to yield an incorrect result, indicating that there might be a misunderstanding in the problem setup. The correct setup should consider the relationship between their ages in 5 years, which is:

F - 5 2(S 5)

Using the correct approach, we find that the son's age S 25 and the father's age F 55.

Conclusion

By solving age-related problems, we can improve our understanding of algebraic equations and their applications. The key to solving such problems is to set up the correct equations and solve them accurately.