Question 974856: Helppppppppppp
explanation and answer please
Kathy stood on the middle rung of a ladder. She climbed up 2 rungs, moved down 5, up then climbed up 6 rugs, and up 4 more to get to the top of the ladder.
How many rungs are there in this ladder?
Found 3 solutions by Alan3354, Edwin McCravy, MathTherapy:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Kathy stood on the middle rung of a ladder. She climbed up 2 rungs, moved down 5, up then climbed up 6 rugs, and up 4 more to get to the top of the ladder.
How many rungs are there in this ladder?
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The other tutor is correct (I think).
Answer by Edwin McCravy(20060)  (Show Source):
You can put this solution on YOUR website!
Kathy stood on the middle rung of a ladder.
That tells us that the ladder has an ODD number of rungs, because if it had
an EVEN number of rungs, there would be no middle rung.
Suppose she started on rung N. Then there were N-1 rungs below her, and
N-1 rungs above her. So altogether on the ladder there are 2(N-1) rungs
plus the 1 middle rung, or 2(N-1)+1 which simplifies to 2N-2+1 or 2N-1
rungs on the ladder.
So she started on the middle rung, which is rung N.
She climbed up 2 rungs,
Then she was on rung N+2
moved down 5,
Then she was on rung N+2 - 5 which simplifies to Rung N-3
then climbed up 6 rugs,
Then she was on rung N-3 + 6 which simplifies to Rung N+3
and up 4 more
Then she was at Rung N+3 + 4 which simplifies to Rung N+7
to get to the top of the ladder.
So she was at rung 2N-1, since the ladder has 2N-1 rungs.
Therefore
N+7 = 2N-1
Solve that and get
8 = N
So the ladder had 2N-1 = 2(8)-1 = 16-1 = 15 rungs,
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Checking:
Kathy stood on the middle rung of a ladder.
Rung 15
Rung 14
Rung 13
Rung 12
Rung 11
Rung 10
Rung 9
Rung 8 <-- She started on the middle rung 8.
Rung 7
Rung 6
Rung 5
Rung 4
Rung 3
Rung 2
Rung 1
She climbed up 2 rungs,
Rung 14
Rung 13
Rung 12
Rung 11
Rung 10 <-- Then she was here. 8+2 = 10
Rung 9
Rung 8
Rung 7
Rung 6
Rung 5
Rung 4
Rung 3
Rung 2
Rung 1
moved down 5,
Rung 15
Rung 14
Rung 13
Rung 12
Rung 11
Rung 10
Rung 9
Rung 8
Rung 7
Rung 6
Rung 5 <-- Then she was here. 10-5 = 5
Rung 4
Rung 3
Rung 2
Rung 1
then climbed up 6 rugs,
Rung 15
Rung 14
Rung 13
Rung 12
Rung 11 <-- then she was here. 5+6 = 11
Rung 10
Rung 9
Rung 8
Rung 7
Rung 6
Rung 5
Rung 4
Rung 3
Rung 2
Rung 1
and up 4 more to get to the top of the ladder.
Rung 15 <-- then she was here at the top of the ladder. 11+4=15. So it checks.
Rung 14
Rung 13
Rung 12
Rung 11
Rung 10
Rung 9
Rung 8
Rung 7
Rung 6
Rung 5
Rung 4
Rung 3
Rung 2
Rung 1
Answer: 15 rungs.
Edwin
Answer by MathTherapy(10552)  (Show Source):
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