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To find the floor where the elevator ends up, we can start at the 10th floor and then add and subtract the corresponding number of floors as the elevator moves.
Starting point: 10
Go down 9 floors: 10 - 9 = 1
Go up 19 floors: 1 + 19 = 20
Go down 3 floors: 20 - 3 = 17
Go down 12 floors: 17 - 12 = 5
Therefore, the elevator ends up on the 5th floor.
We can write an equation to show this calculation:
Starting floor - 9 + 19 - 3 - 12 = Final floor
10 - 9 + 19 - 3 - 12 = 5