Algebra.Com's Answer #796555 by ikleyn(52781)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
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document.write( "I take along a bottle with some wine in it for an excursion in the spring.
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document.write( "On reaching a tavern, I double the bottle’s content and drink 1 9/10 dou in the tavern.
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document.write( "After passing 4 taverns, the bottle is empty. How much wine was there at the beginning?
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document.write( " My interpretation of this problem is different from that of @ankor@dixie-net.com.\r
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document.write( " THEREFORE, my solution and my answer are different.\r
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document.write( "We have a sequence of numbers  ,  ,  ,  ,  .\r\n" );
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document.write( " is the amount of wine in the bottle originally.\r\n" );
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document.write( " is the amount of wine in the bottle at the Exit from the k-th tavern \r\n" );
document.write( " (same as at the entering to the (k+1)-th tavern), k = 1,2,3,4.\r\n" );
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document.write( "From the problem's condition, we have this recursive formula\r\n" );
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document.write( "  =  , (1)\r\n" );
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document.write( "which is the formal mathematical translation of the problem's description.\r\n" );
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document.write( "We are given that = 0, and they want we find .\r\n" );
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document.write( "Surely, the problem should be solved in a backward manner.\r\n" );
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document.write( "For it, I express from (1) in this way\r\n" );
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document.write( " =  (2)\r\n" );
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document.write( "Now I will go step by step BACKWARD from k= 3 with = 0.\r\n" );
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document.write( "In order for to facilitate my calculations, I use MS Excel in my computer with implemented formula (2) in it.\r\n" );
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document.write( "It provides all calculations in seconds, giving me THIS Table below\r\n" );
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document.write( " 4 0\r\n" );
document.write( " 3 0.95\r\n" );
document.write( " 2 1.425\r\n" );
document.write( " 1 1.6625\r\n" );
document.write( " 0 1.78125\r\n" );
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document.write( "So, the ANSWER is: the initial amount of wine in the bottle was 1.78125 units of the volume.\r\n" );
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document.write( "SOLVED.\r
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