Age Puzzles: Solving a Family Age Riddle

Age puzzles are a delightful way to exercise our reasoning skills and explore mathematical concepts. One such puzzle involves a family dynamics problem that requires a bit of algebraic reasoning to solve. Let's delve into the riddle and explore the steps to find the answer.

The Riddle

Let's start with the riddle: when I was 12 years old, my brother was twice my age, and my father was twice my brother's age. Now, I am 20 years old. How old is my father?

Understanding the Problem

To solve this age riddle, we will use algebraic reasoning. We need to assign variables to represent the ages of each member of the family and then set up equations based on the information given.

Step-by-Step Solution

Let's denote the son's age as x.

Given the conditions of the riddle:

When the son is 12 years old: His brother is twice his age: (2 times 12 24) years old. The father is twice his brother's age: (2 times 24 48) years old.

Now, we know that the son is currently 20 years old. Let's set up the equations step-by-step:

Equations and Solution

The son's age 8 years ago (since 20 - 12 8): x - 8. The brother's age 8 years ago: 24 - 8 16. The father's age 8 years ago: 48 - 8 40.

Now, we need to find the father's current age. Since 8 years have passed, we add 8 years to the father's age from 8 years ago:

(40 8 48)

Verification

We can verify the solution by checking if it fits all the given conditions:

The son's age now: (20). The brother's age now: (20 - 8 16 times 2 32). The father's age now: (48 8 56).

Indeed, the solution fits the conditions perfectly, confirming that the father's age is 56 years old.

Conclusion

Solving age puzzles like this one is a great way to practice logical thinking and algebraic reasoning. The answer, as proven, is 56 years old. If you enjoyed this puzzle, try solving more age puzzles to further enhance your problem-solving skills.

Keywords: age puzzle, algebraic reasoning, family age problem, mathematics puzzles, solving math problems