Discovering the Past: The Age Ratio Mystery Unveiled

Delve into the fascinating world of algebraic equations as we solve a riddle about past ages: Ruby is 20 years old and Nazma is 40 years old. How long ago was the ratio of their ages 4:3?

The Riddle

Let’s explore a classic age-related question. Somewhere in the distant past, Ruby’s and Nazma’s ages had a specific ratio of 4:3. Our goal is to find out how many years ago this ratio was observed.

Setting Up the Equation

To solve this riddle, we start by defining x as the number of years in the past when the ratio of their ages was 4:3.

At this point in time:

Ruby's age: 20 - x Nazma's age: 40 - x

The ratio of their ages at that time is given by the equation:

(20 - x): (40 - x) 4:3

Solving the Equation

To solve the equation, we need to clear the fractions and use cross-multiplication to simplify. Let’s go through the steps:

Multiplying the terms to clear the ratio: 3(20 - x) 4(40 - x) Distribute the numbers: 60 - 3x 160 - 4x Move the terms to isolate x: 60 - 3x 4x 160 Combine like terms: 60 x 160 Solve for x: x 100

Conclusion

About 100 years ago, the ages of Ruby and Nazma had the ratio 4:3. This solution bridges the gap between the present and the past, revealing a piece of history through the lens of mathematics.

Related Keywords

age ratio algebraic equations historical ages

Additional Insights

This example not only demonstrates the power of algebra but also encourages us to think about the historical context of our lives. A simple equation can uncover a piece of the past that might otherwise remain hidden. The next time you encounter a similar question, you’ll have the tools to solve it with confidence.