How to Determine the Age of the 4th Child: A Detailed Analysis with Examples

Understanding the average age of a group of children can be a practical tool in various settings, such as schools, family gatherings, or social research. This article provides a step-by-step guide to determine the age of the 4th child based on the average ages of 4 and 3 children. We will also explore a real example and a practical application of this concept.

Understanding the Problem

Given the average age of 4 children is 10 years and the average age of 3 children is 8.5 years, we need to determine the age of the 4th child. Let's break down the problem into manageable steps using mathematical calculations.

Step 1: Convert Averages to Total Ages

We start by converting the given average ages into the total ages of the respective groups of children.

For 4 children:

The average age of 4 children is 10 years. We can express this as:

$$4 times 10 40 , text{years}$$

For 3 children:

The average age of 3 children is 8.5 years. We can express this as:

$$3 times 8.5 25.5 , text{years}$$

Step 2: Calculate the Age of the 4th Child

Next, we find the age of the 4th child by subtracting the total age of the 3 children from the total age of the 4 children.

$$40 - 25.5 14.5 , text{years}$$

Verification and Alternative Solutions

To further verify and ensure the accuracy of our solution, we can use an alternative method. Let's assume the ages of the 4 children are a, b, c, and d.

Example Calculation

Suppose the total age of 4 children is given by the equation:

$$frac{a b c d}{4} 10 , text{years and 7 months}$$

We convert 10 years and 7 months to months:

$$10 times 12 7 127 , text{months}$$

The total age in months for 4 children is:

$$4 times 127 508 , text{months}$$

For 3 Children:

Assuming the total age of 3 children is:

$$frac{a b c}{3} 11 , text{years and 2 months}$$

We convert 11 years and 2 months to months:

$$11 times 12 2 134 , text{months}$$

The total age in months for 3 children is:

$$3 times 134 402 , text{months}$$

The age of the 4th child can then be calculated as:

$$508 - 402 106 , text{months}$$

Converting 106 months back to years and months:

$$106 , text{months} 8 , text{years and 10 months}$$

Practical Application

This method can be applied in various real-life scenarios. For example, if you are organizing a birthday party for a child whose age is the average of a given group of children, you can use this method to determine the exact age.

Conclusion

In summary, the age of the 4th child is 14.5 years in the initial scenario. When solving such problems, it is crucial to convert all ages to a consistent unit (like months) to ensure accurate calculations. Understanding and applying this method can be beneficial in various contexts, making it a valuable tool for both educational and practical purposes.