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

The answer is 10 and here is why.

We don't know how many people were originally on the elevator when Pauline got on, so let's make this unknown a variable, let's say x. Now, follow the trend. Beginning with x amount of people, 4 people get off and 3 get on, on the first stop. This algebraically is x - 4 + 3, which simplifies to x - 1. Now, on the second stop, beginning with x - 1 amount of people, 5 people get off and 1 gets on. This is equal to x - 1 - 5 + 1, which simplifies to x - 6 + 1, which further reduces to x - 5. Now, on the third stop, Pauline gets off, which is equivalent to x - 5 - 1, which simplifies to x - 6. Now, the problem is telling us that 4 people were still remaining on the elevator when Pauline got off. So, whatever amount of people we started off with, when we subtract 6 people from that, it should leave us with 4 people. This is equivalent to x - 6 = 4. Now we use the addition property of equality:

x - 6 + 6 = 4 + 6

Since the 6s on the left side cancel out and 4 + 6 = 10, this leaves us with x = 10. This means that the elevator started out originally with 10 people.