paulina gets on an elevator. at the first stop, 4 people get off and 3 get on. at the second stop, 5 people get off and one gets on. at the third stop, paulina gets off. if 4 people are still in the elevator when paulina gets off, how many people were on the elevator when she got on?

Let x = number of people when she got on.

x -4+3 -5+1 -1 = 4
x -6 = 4
Solve for x to get x=10.
So there were 10 people when Paulina got on (including herself).

the question was how many people were on the elevator when she got on?

6 people

To find out how many people were on the elevator when Paulina got on, we can work backwards and subtract the people who got off and add the people who got on at each stop.

Let's break it down step by step:
- At the first stop, 4 people got off and 3 people got on. So the total change was (-4) + 3 = -1.
- At the second stop, 5 people got off, and 1 person got on. So the total change was (-5) + 1 = -4.
- At the third stop, Paulina gets off, leaving 4 people in the elevator.

Now, if we reverse the changes starting from the third stop, we can find the number of people when she got on:
- At the third stop, since 4 people are still in the elevator, the total change at this stop must be 0 since no one got on or off.
- At the second stop, the total change must be +4 to bring the number of people back up to 4.
- At the first stop, the total change must be +1 to bring the number of people, when Paulina got on, to 5.

So, when Paulina got on the elevator, there were 5 people on it.