document.write( "Question 1190223: a besieged fortress is held by 5700 men who have provisions for 66 days. of the garrison loses 20 men each day, for how many days will be provisions last? \n" ); document.write( "

Algebra.Com's Answer #821841 by Edwin McCravy(20056) $\"\"$ $\"About$

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document.write( "What a gruesome problem! (Men getting killed in war!)\r\n" );
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document.write( "Let K = the number of units of provisions (k-rations] required for 5700 \r\n" );
document.write( "men for 66 days.\r\n" );
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document.write( "Then K/2700 = the number of units of provisions required for 1 man for \r\n" );
document.write( "66 days.\r\n" );
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document.write( "Then K/(2700•66) = the number of units of provisions required for 1 man \r\n" );
document.write( "for 1 day.\r\n" );
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document.write( "If nobody were killed, the sequence over 66 days would be this\r\n" );
document.write( "obvious sum of 66 terms with all identical terms:\r\n" );
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document.write( "However, 20 men are killed each day, so the sequence has more terms and\r\n" );
document.write( "goes like this:\r\n" );
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document.write( "We want to find out how many terms the sequence must have to make \r\n" );
document.write( "the above equation true. \r\n" );
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document.write( "We can divide both sides by K\r\n" );
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document.write( "We can factor out \r\n" );
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document.write( "Suppose the sequence has N terms, then its sum is \r\n" );
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document.write( "       , where a₁=2700, and d=-20\r\n" );
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document.write( "Factor 20 out of the last parentheses on the left\r\n" );
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document.write( "Further simplifying:\r\n" );
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document.write( "N-76 = 0;     N-495 = 0\r\n" );
document.write( "   N = 76;        N = 495\r\n" );
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document.write( "495 is extraneous.\r\n" );
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document.write( "Answer 76 days.\r\n" );
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document.write( "Edwin

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