Math Problem Statement
answer
Solution
To solve this problem, let's analyze the situation step by step:
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Average of A, B, and C is 24 years: So,
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When D joins them, the average age becomes 23 years: So, Substituting ,
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A new person, E, whose age is 3 years more than D (i.e., ), replaces A, and the average of B, C, D, and E becomes 26 years: So, Substituting and ,
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Find the age of A: From and ,
The age of A is 11 years.
Do you want further clarification or details on any step?
Here are some related questions for further practice:
- If the average age of B and C alone is calculated, what is it?
- How would the solution change if E's age was different?
- Can you determine the total combined age of all five individuals (A, B, C, D, E)?
- What happens to the average if D is replaced by someone with an age of 25?
- How would the problem be solved if no replacement occurred but A's age was needed?
Tip: In problems involving averages, always focus on total sums rather than individual averages to simplify calculations.
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Math Problem Analysis
Mathematical Concepts
Averages
Algebra
Basic Arithmetic
Formulas
Average = Sum of terms / Number of terms
Total sum manipulation for averages
Theorems
Basic properties of averages
Suitable Grade Level
Grades 6-8