SOLUTION: lauren was trimming a tree next door. She first moved to the middle rung of her ladder to work, then moved up five rungs, then down seven rungs, and finally back up eleven rungs. A

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: lauren was trimming a tree next door. She first moved to the middle rung of her ladder to work, then moved up five rungs, then down seven rungs, and finally back up eleven rungs. A      Log On


   



Question 908732: lauren was trimming a tree next door. She first moved to the middle rung of her ladder to work, then moved up five rungs, then down seven rungs, and finally back up eleven rungs. At that point she was three rungs from the top of her ladder. How many rungs were im the ladder Lauren used?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = number of rungs on the ladder
Let +1+ = the bottom rung
----------------------------
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:
+%28+n+%2B+1+%29+%2F+2+
------------------
Going up +5+ rungs:
+%28+n%2B1+%29+%2F+2+%2B+5+
Going down +7+ rungs:
+%28+n%2B1+%29+%2F+2+%2B+5+-+7+
And up +11+ rungs
+%28+n+%2B+1+%29+%2F+2+%2B+5+-+7+%2B+11+
-----------------------------
She was then located at:
+n+-+3+, so
+%28+n+%2B+1+%29+%2F+2+%2B+9+=+n+-+3+
Multiply both sides by +2+
+n+%2B+1+%2B+18+=+2n+-+6+
+n+=+19+%2B+6+
+n+=+25+
There were 25 rungs on the ladder
check:
She started at:
+%28+25+%2B+1+%29+%2F+2+=+13+
Up +5+ rungs:
+13+%2B+5+=+18+
Down +7+ rungs:
+18+-+7+=+11+
Up +11+ rungs:
+11+%2B+11+=+22+
She is +3+ rungs from the top, since
+22+%2B+3+=+25+
OK