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?
I need to find the number of people in the room, which I'll call P. I also need to find the number of chairs in the room, which I'll call C. I know that two-thirds of the people are seated in three-fourths of the chairs, so I can write an equation for that: (2/3)P = (3/4)C. I also know that there are 6 empty chairs, which means that one-fourth of the chairs are empty, so I can write another equation for that: (1/4)C = 6. Now I have two equations with two unknowns, so I can try to solve for P and C. I can start by multiplying both sides of the second equation by 4 to get C = 24. That means there are 24 chairs in the room. Then I can plug that value into the first equation and simplify: (2/3)P = (3/4)C, (2/3)P = (3/4)(24), (2/3)P = 18, P = 18 * (3/2), P = 27. So there are 27 people in the room. 