Solving the Ratio of Ages: A Comprehensive Guide

Understanding and solving age-related problems, particularly those involving ratios, is a fundamental skill in mathematics. This article provides a detailed step-by-step guide to solving a specific age-related problem, helping you to understand and solve similar problems in the future.

Problem Statement

The ages of A, B, and C are in the ratio 4:5:6. If the sum of their ages is 75 years, what is the age of C?

Solution

To solve this problem, we will follow a structured approach:

Step 1: Understanding the Problem

We are given the ratio of the ages of A, B, and C as 4:5:6. This means:

The age of A is 4 parts. The age of B is 5 parts. The age of C is 6 parts.

Let's denote the common factor by 'x'. Therefore, the ages can be represented as:

Age of A 4x Age of B 5x Age of C 6x

Step 2: Setting Up the Equation

The problem states that the sum of their ages is 75 years. Therefore, we can set up the equation:

4x 5x 6x 75

Combining the like terms on the left side, we get:

15x 75

To find the value of x, we will divide both sides of the equation by 15:

x 75 / 15

x 5

Step 3: Calculating the Age of C

Now, we know that the age of C is 6x. Substituting the value of x, we get:

Age of C 6 * 5 30 years

Alternative Method (Alternative Solution)

Another way to solve this problem is to directly use the given sum and the total parts of the ratio:

15 parts of the ratio represent 75 years. Therefore:

Age of C (6/15) * 75

Age of C 6 * 5 30 years

Conclusion

The age of C is 30 years. This method can be applied to similar problems where you are given the ratio of ages and the total sum of ages.

Additional Resources

If you would like to learn more about solving age-related problems or need additional practice, consider revisiting the concept of ratio and proportion. Utilizing online resources or educational platforms can provide you with further practice problems and detailed explanations.

Note: This guide is designed to help you solve such problems efficiently. If you have any questions or need further assistance, feel free to ask!