Solving the Age Puzzle: When I Was 5, My Sister Was Double My Age

Have you ever come across a math puzzle where your sister's age is described in relation to your age? It can be quite a brain teaser, but with a step-by-step approach, it can be solved easily. Let's explore the problem and see how to determine the sister's current age.

The Problem Statement

When I was 5 years old, my sister was double of my age. Now I am 6 years old, how old is my sister?

Analyzing the Problem

To solve this, let's start by breaking down the information given:

You were 5 years old. Your sister was double of your age, which means she was 10 years old. You are now 6 years old.

Mathematical Approach

Let 'x' be your sister's current age. We can set up the following equation based on the information given:

Step 1: Establish the age difference

The age difference between the sister and you has been constant over the years. When you were 5, she was 10.

Step 2: Set up the equation

Your sister's current age minus your current age should be equal to the age difference that you already established.

Your sister's age (x) - Your age (6) Age difference (10 - 5 5) Therefore, x - 6 5

Step 3: Solve for x

Let's solve the equation:

x - 6 5 x 5 6 x 11

However, this step reconstructs the initial condition. Let's reframe the equation with the correct ages:

Your sister's age (x) - Your current age (6) Age difference (as of the initial condition, she was 5 years younger than double your age 10 - 5 5) x - 6 5 x 6 5 x 11

This is incorrect. Let's correct it by looking at the correct ages:

Your sister's age (x) - Your current age (6) Age difference (which is 5 - because your sister was 10 - 5 years old, 5 years before you were 5) x - 6 5 x 6 5 x 11

So, your sister is 48 years old now.

Conclusion

Hence, if you are now 45 years old, and you were 5 when your sister was 10 (which is 5 years older than you), then she is 3 years older. Therefore, if you are 45, your sister is 45 3 48.

Verification with Mathematicians

Mathematicians and puzzle solvers often use this method to solve similar problems:

Let Syour sister's current age Let Yyour current age S-Y3 years Assuming S45 (Your age now), solve for S: S-453 S45 3 S48