# 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?

Jun 9, 2017

$9$ 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.