document.write( "Question 905637: Anna writes a list of positive integers that are not necessarily
\n" ); document.write( "all different. She, of course, includes her favorite number 68 on the list. the mean of all of the numbers is 56. Then, Alex erases a 68. The
\n" ); document.write( "mean of the remaining numbers is 55.
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Algebra.Com's Answer #549302 by Edwin McCravy(20060) $\"\"$ $\"About$

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Anna writes a list of positive integers that are not necessarily
\n" ); document.write( "all different. She, of course, includes her favorite number 68 on
\n" ); document.write( "the list. the mean of all of the numbers is 56. Then, Alex erases
\n" ); document.write( "a 68. The mean of the remaining numbers is 55.
\n" ); document.write( "What is the largest number that could be on the list?
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document.write( "Let s = the sum of all the positive integers besides the 68.\r\n" );
document.write( "Let n = the number of positive integers\r\n" );
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document.write( "Then \r\n" );
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document.write( "or\r\n" );
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document.write( "or\r\n" );
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document.write( "After Alex erases the 68, there are only n-1 positive integers,\r\n" );
document.write( "with sum s and average 55, so\r\n" );
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document.write( "or\r\n" );
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document.write( "or\r\n" );
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document.write( "or\r\n" );
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document.write( "Solve the system\r\n" );
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document.write( "The solution is s = 660, n=13\r\n" );
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document.write( "So there are 13 positive integers, counting the 68.\r\n" );
document.write( "So the other 12 positive integers have sum 660.\r\n" );
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document.write( "The largest possible positive integer in the list would\r\n" );
document.write( "be when 11 of the 12 positive integers other than 68 are\r\n" );
document.write( "as small as a positive integer can be, which is 1.  So \r\n" );
document.write( "that would be when 11 of the others beside the 68 are \r\n" );
document.write( "all 1's and one of them is 660-11 = 649.\r\n" );
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document.write( "Answer: 649\r\n" );
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document.write( "Edwin

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