2007 AMC 8 Problem 7

Attempt Problem 7 of the 2007 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2007 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

7.

The average age of 55 people in a room is 3030 years. An 1818-year-old person leaves the room. What is the average age of the four remaining people?
2525
2626
2929
3333
3636
Answer: D
Concepts:mean
Small hint:
Convert the original average into a total age.
Big hint:
Subtract the age of the person who leaves before dividing by the remaining number of people.
Solution:
Initially, the total age of everyone in the room is 5⋅30=1505 \cdot 30 = 150 years.
After the person leaves, the total age is 150−18=132.150 - 18 = 132. With 44 people remaining, the average age becomes 1324=33.\dfrac{132}{4} = 33.
Thus, D is the correct answer.
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