document.write( "Question 974856: Helppppppppppp
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\n" ); document.write( "\n" ); document.write( "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.\r
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Algebra.Com's Answer #596676 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "Kathy stood on the middle rung of a ladder.
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document.write( "That tells us that the ladder has an ODD number of rungs, because if it had\r\n" );
document.write( "an EVEN number of rungs, there would be no middle rung.\r\n" );
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document.write( "Suppose she started on rung N. Then there were N-1 rungs below her, and\r\n" );
document.write( "N-1 rungs above her.  So altogether on the ladder there are 2(N-1) rungs\r\n" );
document.write( "plus the 1 middle rung, or 2(N-1)+1 which simplifies to 2N-2+1 or 2N-1\r\n" );
document.write( "rungs on the ladder.  \r\n" );
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document.write( "So she started on the middle rung, which is rung N. \r\n" );
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\n" ); document.write( "She climbed up 2 rungs,
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document.write( "Then she was on rung N+2\r\n" );
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\n" ); document.write( "moved down 5,
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document.write( "Then she was on rung N+2 - 5 which simplifies to Rung N-3\r\n" );
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\n" ); document.write( "then climbed up 6 rugs,
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document.write( "Then she was on rung N-3 + 6 which simplifies to Rung N+3\r\n" );
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\n" ); document.write( "and up 4 more
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document.write( "Then she was at Rung N+3 + 4 which simplifies to Rung N+7\r\n" );
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\n" ); document.write( "to get to the top of the ladder.
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document.write( "So she was at rung 2N-1, since the ladder has 2N-1 rungs.\r\n" );
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document.write( "Therefore\r\n" );
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document.write( "N+7 = 2N-1\r\n" );
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document.write( "Solve that and get\r\n" );
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document.write( "8 = N\r\n" );
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document.write( "So the ladder had 2N-1 = 2(8)-1 = 16-1 = 15 rungs,\r\n" );
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document.write( "Checking:\r\n" );
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document.write( "Kathy stood on the middle rung of a ladder. \r\n" );
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document.write( "Rung 15\r\n" );
document.write( "Rung 14\r\n" );
document.write( "Rung 13\r\n" );
document.write( "Rung 12\r\n" );
document.write( "Rung 11\r\n" );
document.write( "Rung 10\r\n" );
document.write( "Rung 9\r\n" );
document.write( "Rung 8  <-- She started on the middle rung 8.\r\n" );
document.write( "Rung 7\r\n" );
document.write( "Rung 6\r\n" );
document.write( "Rung 5\r\n" );
document.write( "Rung 4\r\n" );
document.write( "Rung 3\r\n" );
document.write( "Rung 2\r\n" );
document.write( "Rung 1\r\n" );
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document.write( "She climbed up 2 rungs, \r\n" );
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document.write( "Rung 14\r\n" );
document.write( "Rung 13\r\n" );
document.write( "Rung 12\r\n" );
document.write( "Rung 11\r\n" );
document.write( "Rung 10  <-- Then she was here. 8+2 = 10\r\n" );
document.write( "Rung 9   \r\n" );
document.write( "Rung 8\r\n" );
document.write( "Rung 7   \r\n" );
document.write( "Rung 6\r\n" );
document.write( "Rung 5\r\n" );
document.write( "Rung 4\r\n" );
document.write( "Rung 3\r\n" );
document.write( "Rung 2\r\n" );
document.write( "Rung 1\r\n" );
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document.write( "moved down 5, \r\n" );
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document.write( "Rung 15\r\n" );
document.write( "Rung 14\r\n" );
document.write( "Rung 13\r\n" );
document.write( "Rung 12\r\n" );
document.write( "Rung 11\r\n" );
document.write( "Rung 10\r\n" );
document.write( "Rung 9\r\n" );
document.write( "Rung 8\r\n" );
document.write( "Rung 7   \r\n" );
document.write( "Rung 6\r\n" );
document.write( "Rung 5  <-- Then she was here. 10-5 = 5\r\n" );
document.write( "Rung 4\r\n" );
document.write( "Rung 3\r\n" );
document.write( "Rung 2\r\n" );
document.write( "Rung 1\r\n" );
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document.write( "then climbed up 6 rugs, \r\n" );
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document.write( "Rung 15\r\n" );
document.write( "Rung 14\r\n" );
document.write( "Rung 13\r\n" );
document.write( "Rung 12\r\n" );
document.write( "Rung 11  <-- then she was here. 5+6 = 11 \r\n" );
document.write( "Rung 10\r\n" );
document.write( "Rung 9\r\n" );
document.write( "Rung 8\r\n" );
document.write( "Rung 7   \r\n" );
document.write( "Rung 6\r\n" );
document.write( "Rung 5\r\n" );
document.write( "Rung 4\r\n" );
document.write( "Rung 3\r\n" );
document.write( "Rung 2\r\n" );
document.write( "Rung 1\r\n" );
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document.write( "and up 4 more to get to the top of the ladder.\r\n" );
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document.write( "Rung 15  <-- then she was here at the top of the ladder. 11+4=15.  So it checks.\r\n" );
document.write( "Rung 14\r\n" );
document.write( "Rung 13\r\n" );
document.write( "Rung 12\r\n" );
document.write( "Rung 11\r\n" );
document.write( "Rung 10\r\n" );
document.write( "Rung 9\r\n" );
document.write( "Rung 8\r\n" );
document.write( "Rung 7   \r\n" );
document.write( "Rung 6\r\n" );
document.write( "Rung 5\r\n" );
document.write( "Rung 4\r\n" );
document.write( "Rung 3\r\n" );
document.write( "Rung 2\r\n" );
document.write( "Rung 1  \r\n" );
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document.write( "Answer: 15 rungs.\r\n" );
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document.write( "Edwin
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