2004 AMC 8 Problem 20
Attempt Problem 20 of the 2004 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 2004 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
20.
Two-thirds of the people in a room are seated in three-fourths of the chairs. The rest of the people are standing. If there are empty chairs, how many people are in the room?
Answer: D
Small hint:
The empty chairs are the remaining one-fourth of the chairs.
Big hint:
The seated people are two-thirds of all the people.
Solution:
Since of the chairs are occupied, the empty chairs are of all the chairs. Thus there are chairs.
The number of seated people is of which is
Those seated people are of all the people, so the total number of people is
Thus, D is the correct answer.
Problem 20 in other years
- 1985 AMC 8
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