Question 908732
Let {{{ n }}} = number of rungs on the ladder
Let {{{ 1 }}} = the bottom rung
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There is a middle rung, so that means
there must be an odd number of rungs, since
an even number would have no middle rung
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The middle rung is located at:
{{{ ( n + 1 ) / 2 }}} 
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Going up {{{ 5 }}} rungs:
{{{ ( n+1 ) / 2 + 5 }}}
Going down {{{ 7 }}} rungs:
{{{ ( n+1 ) / 2 + 5 - 7 }}}
And up {{{ 11 }}} rungs
{{{ ( n + 1 ) / 2 + 5 - 7 + 11 }}}
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She was then located at:
{{{ n - 3 }}}, so
{{{ ( n + 1 ) / 2 + 9 = n - 3 }}}
Multiply both sides by {{{ 2 }}}
{{{ n + 1 + 18 = 2n - 6 }}}
{{{ n = 19 + 6 }}}
{{{ n = 25 }}}
There were 25 rungs on the ladder
check:
She started at:
{{{ ( 25 + 1 ) / 2 = 13 }}}
Up {{{ 5 }}} rungs:
{{{ 13 + 5 = 18 }}}
Down {{{ 7 }}} rungs:
{{{ 18 - 7 = 11 }}}
Up {{{ 11 }}} rungs:
{{{ 11 + 11 = 22 }}}
She is {{{ 3 }}} rungs from the top, since
{{{ 22 + 3 = 25 }}}
OK