Question

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?

Answer 1

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.