document.write( "Question 333945: Find all sets of three consecutive odd integers whose sum is between 20 and 30. \n" ); document.write( "

Algebra.Com's Answer #239293 by Edwin McCravy(20054) $\"\"$ $\"About$

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Find all sets of three consecutive odd integers whose sum is between 20 and 30.
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document.write( "The statement is not entirely clear as to whether the sum is to be \r\n" );
document.write( "'inclusive' or 'excusive' of the two bounds. But it won't even matter,\r\n" );
document.write( "because the sum of three odd integers must be odd, so it's definitely\r\n" );
document.write( "exclusive.\r\n" );
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document.write( "What we require is this:\r\n" );
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document.write( "20 < n + (n+2) + (n+4) < 30\r\n" );
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document.write( "Remove the parentheses\r\n" );
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document.write( "20 <  n + n + 2 + n + 4 < 30\r\n" );
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document.write( "Collect like terms\r\n" );
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document.write( "     20 < 3n + 6 < 30\r\n" );
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document.write( "Add -6 to all three sides:\r\n" );
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document.write( "     20 < 3n + 6 < 30\r\n" );
document.write( "     -6       -6   -6\r\n" );
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document.write( "     14 < 3n     < 24\r\n" );
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document.write( "     < n < 8\r\n" );
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document.write( "    < n < 8  \r\n" );
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document.write( "The only odd integers that satify that are 5 and 7  \r\n" );
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document.write( "So the only sets of three consecutive integers with a\r\n" );
document.write( "sum in that domain are: \r\n" );
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document.write( "{5, 7, 9}, since 5 + 7 + 9 = 21\r\n" );
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document.write( "{7, 9, 11}, since 7 + 9 + 11 = 27\r\n" );
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document.write( "Edwin

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