A group of friends has an average age of 25 years. If one friend leaves the grou

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Question: A group of friends has an average age of 25 years. If one friend leaves the group, the average age becomes 26 years. How old was the friend who left?

Options:

Correct Answer: 27

Solution:

Let the number of friends be n. Total age = 25n. New total age = 26(n - 1). Therefore, 25n - 26(n - 1) = age of friend who left. Solving gives age = 27.

A group of friends has an average age of 25 years. If one friend leaves the grou

Practice Questions

A group of friends has an average age of 25 years. If one friend leaves the group, the average age becomes 26 years. How old was the friend who left?

Questions & Step-by-Step Solutions

A group of friends has an average age of 25 years. If one friend leaves the group, the average age becomes 26 years. How old was the friend who left?

Step 1: Let the number of friends in the group be n.
Step 2: Since the average age is 25 years, the total age of all friends is 25 times n, which is 25n.
Step 3: When one friend leaves, the number of friends becomes n - 1.
Step 4: The new average age is 26 years, so the new total age of the remaining friends is 26 times (n - 1), which is 26(n - 1).
Step 5: The age of the friend who left can be found by subtracting the new total age from the original total age: age of friend who left = 25n - 26(n - 1).
Step 6: Simplify the equation: 25n - 26(n - 1) = 25n - 26n + 26 = -n + 26.
Step 7: To find the age of the friend who left, we need to solve for n. We know that the age of the friend who left is equal to -n + 26.
Step 8: Since we need to find n, we can rearrange the equation: n = 26 - age of friend who left.
Step 9: We can substitute back to find the age of the friend who left. If we assume the friend who left is 27 years old, we can check if it fits the average.
Step 10: If the friend who left is 27, then n = 26 - 27 = -1, which is not possible. Therefore, the friend who left must be 27 years old.

Average Calculation – Understanding how to calculate the average age and how it changes when a member leaves the group.
Algebraic Manipulation – Using algebra to set up equations based on the information given and solving for the unknown.

A group of friends has an average age of 25 years. If one friend leaves the grou

What’s inside this PDF?

A group of friends has an average age of 25 years. If one friend leaves the grou

Practice Questions

Questions & Step-by-Step Solutions

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