Charlie entered an elevator and ride up 10 floors and then down 2 floors before realizing he had not pressed the button for Floor 1. He then pressed the button for Floor 1 and rode down 14 floors and exited the elevator on Floor 1. On which floor did he begin?

Floor 7

Step-by-step explanation:

He entered the elevator on floor x.

Then he rode up 10 floors. Now he is on floor x + 10.

Then he rode down 2 floors. Now he is on floor x + 10 - 2 = x + 8.

Then he pressed the Floor 1 button and rode down 14 floors to Floor 1. Now he is on floor x + 8 - 14 = x - 6 which is the same as Floor 1.

Floor x - 6 is the same as Floor 1, so we get the equation:

x - 6 = 1

Add 6 to both sides:

x = 7

Since we let x be the floor number he entered the elevator in, he entered the elevator on Floor 7.

He began on floor 7

Step-by-step explanation:

This is a question where you have to use the question from the end and work your way backwards if that makes sense.

He had to go down 14 floors to get to floor 1. So 14 + 1 = 15. He was on the 15th floor.

Next he went down 2 floors. Since this is reverse, add two floors to the answer. 15 + 2 = 17. He was on the 17th floor.

And finally, he goes up 10 floors. Doing this in reverse, take away 10 floors to the answer. 17 - 10 = 7

He started on the 7th floor.

Now to make sure it is correct, start from 7 and follow the original order of the question.

7 + 10 = 17

17 - 2 = 15

15 - 14 = 1