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?

1 Answer
SoySoy4444
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.

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