Question

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 $6$ empty chairs, how many people are in the room?

$12$

$18$

$24$

$27$

$36$

Solution:

Since $3/4$ of the chairs are occupied, the $6$ empty chairs are $1/4$ of all the chairs. Thus there are $24$ chairs.

The number of seated people is $3/4$ of $24$ , which is $18$ .

Those $18$ seated people are $2/3$ of all the people, so the total number of people is $18\div\frac23=27$ .

Thus, D is the correct answer.

2004 AMC 8 Problem 20

Solution:

Problem 20 in Other Years