Problem 10 · 2008 AMC 8
Easy
Arithmetic & Operations
weighted-average
The average age of the 6 people in Room A is 40. The average age of the 4 people in Room B is 25. If the two groups are combined, what is the average age of all the people?
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Answer: D — 34.
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Hint 1 of 2
You can't just average 40 and 25 — Room A has more people, so it pulls the result toward 40.
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Hint 2 of 2
Rebuild each total with total = average × count, then pool everything: combined average = all ages ÷ all people.
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Approach: recover totals, then pool
- An average hides a total: Room A is 6 · 40 = 240 years, Room B is 4 · 25 = 100 years. Now you have real piles you can combine.
- Pool them: 340 years across 10 people = 340 ÷ 10 = 34.
- Why this transfers: the naive midpoint (40+25)÷2 = 32.5 is the trap answer A — a combined average leans toward the bigger group, so it lands at 34, closer to 40.
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