The average age of a twelve-member team is the same as it was 4 years ago, because an old member has been replaced by a young member. If the age of older member is 65 What is the age of young member?

Let's denote the average age of the twelve-member team 4 years ago as \( A \).

1. **Total age 4 years ago**: The total age of the team 4 years ago was \( 12A \).

2. **Total age now**: Since the average age remains the same, the total age of the team now is also \( 12A \).

3. **Aging effect over 4 years**: Over the last 4 years, each of the 11 members who remained on the team has aged 4 years. Thus, the total increase in their ages is \( 11 \times 4 = 44 \) years.

4. **Replacement effect**: The old member (65 years old) has been replaced by a young member. Let's denote the age of the young member as \( x \).

Given that the total age remains \( 12A \), the equation is:

\[
12A + 44 - 65 + x = 12A
\]

Simplifying the equation:

\[
44 - 65 + x = 0
\]

\[
x = 65 - 44
\]

\[
x = 21
\]

So, the age of the young member is **21 years**.

Do you want more details, or do you have any questions?

Here are 5 related questions to consider:
1. How would the average age change if another member is replaced similarly?
2. What if the team's size was different, say 10 members? How would the calculation differ?
3. How do you calculate the average age if the team's ages were explicitly given?
4. What happens to the average if a member of the team leaves but is not replaced?
5. Can you find the total sum of the team members' ages without knowing the average?

**Tip:** Always keep track of changes in total age when dealing with averages, as it can greatly simplify your calculations.

Explore how to calculate the age of a young member in a twelve-member team where an older member has been replaced. Follow a step-by-step solution involving averages and arithmetic. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation