# Kathy stood on the middle rung of a ladder. She climbed up 5 rungs, moved down 2 rungs, and then climbed up 7 rungs. Then she climbed up the remaining 2 rungs to the top of the ladder. How many rungs are there in the whole ladder?

Kathy stood on the middle rung of a ladder. She climbed up 5 rungs, moved down 2 rungs, and then climbed up 7 rungs. Then she climbed up the remaining 2 rungs to the top of the ladder. How many rungs are there in the whole ladder?
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Everett Melton
Number of rung of the ladder must be odd, because starts in the middle rung. The number of rungs on the ladder is some number, 2n+1 for some whole number 2.
The middle rung (t):
$\frac{2n+1}{2}+\frac{1}{2}$
The start $t+5-2+7+2\phantom{\rule{0ex}{0ex}}=t+12\phantom{\rule{0ex}{0ex}}\left(\frac{2n+1}{2}+\frac{1}{2}\right)+12=2n+1\phantom{\rule{0ex}{0ex}}⇒\frac{2n+1}{2}-2n=1-12-\frac{1}{2}\phantom{\rule{0ex}{0ex}}⇒\frac{2n+1-4n}{2}=\frac{-23}{2}\phantom{\rule{0ex}{0ex}}⇒-2n+1=-23\phantom{\rule{0ex}{0ex}}⇒2n-1=23\phantom{\rule{0ex}{0ex}}⇒2n=24⇒n=12$
Number of rungs $\left(2n+1\right)=\phantom{\rule{0ex}{0ex}}2×12+1=25$
There are 25 rungs on the ladder.