SOLUTION: Kathy stood on the middle rung of a ladder. She climbed up 2 rings, moved down 3 rings and then climbed up 7 rings. Then she climbed up the remaining 2 rings to the top of the ladd

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Question 1064569: Kathy stood on the middle rung of a ladder. She climbed up 2 rings, moved down 3 rings and then climbed up 7 rings. Then she climbed up the remaining 2 rings to the top of the ladder. How many rings are there in the whole ladder?
Found 4 solutions by stanbon, josmiceli, josgarithmetic, MathTherapy:
Answer by stanbon(75887) About Me  (Show Source):
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Kathy stood on the middle rung of a ladder. She climbed up 2 rings, moved down 3 rings and then climbed up 7 rings. Then she climbed up the remaining 2 rings to the top of the ladder. How many rings are there in the whole ladder?
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start:: middle rung
middle + 2 -3 + 7 = middle + 6
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Ans: middle + 6 above + 6 below
# of rungs = 1 + 12 = 13
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Cheers,
Stan H.
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Answer by josmiceli(19441) About Me  (Show Source):
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Let +n+ = the number of rungs from
the middle to the top
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After climbing up 2 rungs, there are
+n+-+2+ rungs left to the top
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She climbed down +3+ rungs,
there are +n+-+2+%2B+3+=+n+%2B+1+
rungs to the top
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She climbed up +7+ rungs
There are +n+%2B+1+-+7+=+n+-+6+
rungs to the top
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There are +2+ rungs to the top, so I can say:
+n+-+6+=+2+
+n+=+8+
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There are +8+ rungs from the middle to the top
I can't count the middle rung twice, so ther are
+n+-+1+=+8+-+1+
+n+-+1+=+7+ rungs to the bottom
+n+%2B+%28+n+-+1+%29+=+8+%2B+7+
+8+%2B+7+=+15+
There are 15 rungs on the whole ladder
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Check my math & maybe get another opinion, too

Answer by josgarithmetic(39623) About Me  (Show Source):
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Number of rungs on 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 n.

The MIDDLE rung:
%282n%2B1%29%2F2%2B1%2F2


The description of the movements:
theStart%2B2-3%2B7%2B2
theStart%2B8, to reach the top rung.



%28%282n%2B1%29%2F2%2B1%2F2%29%2B8=2n%2B1
Solve for n and evaluate 2n+1.

%282n%2B1%29%2F2-2n=1-8-1%2F2

2n-%282n%2B1%29%2F2=8-1%2B1%2F2

2n-%282n%2B1%29%2F2=7%2B1%2F2

4n-2n-1=15

2n-1=15

2n=16

highlight%28n=8%29

Number of rungs, 2n%2B1
2%2A8%2B1
highlight%2817%29

Answer by MathTherapy(10555) About Me  (Show Source):
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Kathy stood on the middle rung of a ladder. She climbed up 2 rings, moved down 3 rings and then climbed up 7 rings. Then she climbed up the remaining 2 rings to the top of the ladder. How many rings are there in the whole ladder? 
Let number of rungs be R

Standing on the middle rung, there are equal number of rungs above her and below her

Thus, she’s standing on the MEDIAN rung, or the %28R+%2B+1%29%2F2 rung

We then get: %28R+%2B+1%29%2F2+%2B+2+-+3+%2B+7+%2B+2+=+R

%28R+%2B+1%29%2F2+%2B+8+=+R

R + 1 + 16 = 2R ------ Multiplying by LCD, 2

17 = 2R – R

R, or number of rungs = highlight_green%2817%29