Understanding the Family Average Age Problem

This question involves calculating the age of a new member added to a family based on the change in the family's average age. The average age is the sum of the ages of all members divided by the number of members.

Let's break down the information given:

• Initially, there are 3 family members (Mother, Father, Son).
• The average age of these 3 members is 44 years.
• After the son's marriage, a new member (Daughter-in-law) joins the family, making it 4 members.
• The new average age of the 4 members is 39 years.

Step-by-Step Solution for Calculating Age

To find the age of the daughter-in-law, we first need to calculate the total sum of ages in both scenarios.

Step 1: Calculate the initial total age of the family

The initial family has 3 members, and their average age is 44 years. The sum of their ages is calculated as:

Sum of ages = Average age $\times$ Number of members

Initial sum of ages $= 44 \text{ years} \times 3 = 132 \text{ years}$

So, the combined age of the Mother, Father, and Son is 132 years.

Step 2: Calculate the total age of the family after the son's marriage

After the son's marriage, the family has 4 members, and their average age is 39 years. The sum of their ages is calculated as:

Sum of ages = Average age $\times$ Number of members

Sum of ages after marriage $= 39 \text{ years} \times 4 = 156 \text{ years}$

So, the combined age of the Mother, Father, Son, and Daughter-in-law is 156 years.

Step 3: Calculate the age of the daughter-in-law

The difference between the total age of the family after the marriage and the initial total age is the age of the new member (the daughter-in-law).

Age of Daughter-in-law = Sum of ages after marriage - Initial sum of ages

Age of Daughter-in-law $= 156 \text{ years} - 132 \text{ years}$

Age of Daughter-in-law $= 24 \text{ years}$

Therefore, the age of the daughter-in-law is 24 years.

Summary of Calculations

Age of Daughter-in-law = Total Age (After Marriage) - Total Age (Initial)

Age of Daughter-in-law = $156 - 132 = 24$ years.

Conclusion on Daughter-in-law's Age

Based on the calculations, the age of the daughter-in-law is 24 years. This matches option 1.

Revision Table: Family Age Problem

Additional Information: Average Calculation Tips

Understanding averages is fundamental in many quantitative problems. Here are some key points:

• The average represents a central value in a set of numbers.
• When a new member is added to a group, the average can change. If the new member's value (age in this case) is higher than the current average, the average increases. If it's lower, the average decreases. If it's equal, the average stays the same.
• In this problem, the average age decreased from 44 to 39 when the daughter-in-law joined. This implies the daughter-in-law's age must be less than the initial average age of 44. Let's verify: 24 is indeed less than 44.
• Calculating the total sum is often the first step when dealing with average problems involving changes in the number of members or the average itself.