A father says to his son, "I was as old as you are now at the time of your birth."\nIf the father is 38 years old at present, what was the age of the son 5 years ago?

Introduction / Context:
This is a classic age puzzle that involves relating present ages to ages at a past event, namely the sons birth. It tests your ability to translate words into algebraic equations and then compute the required age.

Given Data / Assumptions:

• Present age of the father = 38 years.
• Present age of the son = x years (unknown).
• At the time of the sons birth, the father was as old as the son is now.
• We are asked to find the sons age 5 years ago.

Concept / Approach:
If the son is x years old now, then the sons birth occurred x years ago. At that time, the father was 38 - x years old. According to the statement, that age of the father equals the son s current age x. This gives an equation which we can solve for x. After finding x, we subtract 5 years to get the sons age five years ago.

Step-by-Step Solution:
Let the sons present age = x years. The son was born x years ago. At that time, the father s age = 38 - x years. Given: 38 - x = x. So 38 = 2x. Therefore x = 19. Sons present age = 19 years. Sons age 5 years ago = 19 - 5 = 14 years. So the son was 14 years old five years ago.

Verification / Alternative check:
If the son is 19 now, his birth was 19 years ago. At that time, the father s age would have been 38 - 19 = 19 years, which matches the sons present age. This fits the father s statement perfectly, confirming that the calculation is correct.

Why Other Options Are Wrong:
Option 19 is the sons present age, not his age five years ago. Option 33 would imply an impossible negative age at birth for the father. Option 38 is the father s present age and does not relate to the sons age five years ago.

Common Pitfalls:
Students sometimes equate the wrong ages, for example taking the son s present age as the father s present age at birth, which makes no sense. Another error is forgetting to subtract the 5 years at the end and stopping at the present age of the son. Carefully track the time shifts and which age is being discussed at each point in time.

Final Answer:
The sons age five years ago was 14 years.