Question

Cheryl climbed a set of stairs and stopped at the middle step. She then walked down 2 steps, up 4 steps, down 3 steps, and up 5 steps, and she was at the top of the stairs. How many steps are in the set of stairs?

Answer 1

`9` steps

Explanation:

We know that Cheryl was at the middle of the set of stairs. Let the middle step be `x`.

Since she walked down 2 steps, that can be modelled as `x-2`
We continue modelling it, until we get

`x-2+4-3+5`
`=x+4`

Therefore, from the middle of the set of stairs to the top, there are 4 steps. That means that since `x` is the median of the set of steps, it follows that there are also `4` steps from the middle to the lowest step.

Therefore, including the middle step, we have `4+4+1=9` steps in total.