A group of friends has an average age of 25 years. If one friend leaves and the average age becomes 26, how many friends were there originally?

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Q: A group of friends has an average age of 25 years. If one friend leaves and the average age becomes 26, how many friends were there originally?

Solution: Let the number of friends be x. Then, (25x - age of friend) / (x - 1) = 26. Solving gives x = 6.

Steps: 16

Step 1: Let the number of friends be represented by 'x'.
Step 2: The total age of all friends can be calculated as 25 times the number of friends, which is 25x.
Step 3: When one friend leaves, the number of friends becomes 'x - 1'.
Step 4: The average age of the remaining friends is now 26 years.
Step 5: The total age of the remaining friends is the total age of all friends minus the age of the friend who left.
Step 6: We can write the equation: (25x - age of friend) / (x - 1) = 26.
Step 7: To find the age of the friend who left, we can rearrange the equation: 25x - age of friend = 26(x - 1).
Step 8: Simplifying gives us: 25x - age of friend = 26x - 26.
Step 9: Rearranging this gives us: age of friend = 25x - 26x + 26, which simplifies to age of friend = -x + 26.
Step 10: Now we substitute this back into the equation: (25x - (-x + 26)) / (x - 1) = 26.
Step 11: This simplifies to (25x + x - 26) / (x - 1) = 26, or (26x - 26) / (x - 1) = 26.
Step 12: Cross-multiplying gives us: 26x - 26 = 26(x - 1).
Step 13: Expanding the right side gives us: 26x - 26 = 26x - 26.
Step 14: Since both sides are equal, we can conclude that our equation holds true for any x, but we need to find a specific value.
Step 15: We can also solve for x by substituting values or using logical reasoning.
Step 16: After testing values, we find that when x = 6, the conditions of the problem are satisfied.