document.write( "Question 1163645: The sum of two whole numbers is 45 and their difference is less than 10. The numbers of all possible pairs is? \n" ); document.write( "

Algebra.Com's Answer #787805 by ikleyn(52838) $\"\"$ $\"About$

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document.write( "The possible pairs are (x,45-x)  with  the conditions\r\n" );
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document.write( "    x is whole, 45 -x is whole and  | x - (45-x) | < 10.      (1)\r\n" );
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document.write( "I use the absolute value inequality, based on the context, saying \"their difference\", which means both possible differences.\r\n" );
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document.write( "In other words, the numbers are (x,45-x), where\r\n" );
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document.write( "    x is integer, 0 <= x <= 45  and  -10 < 2x -45 < 10.       (2)\r\n" );
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document.write( "The last compound inequality means\r\n" );
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document.write( "     -10 + 45 < 2x < 10 + 45.\r\n" );
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document.write( "     35       < 2x < 55\r\n" );
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document.write( "     17.5     < x < 27.5.                                     (3)\r\n" );
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document.write( "There are 10 integer solutions for the last compound inequality\r\n" );
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document.write( "     x = 18, 19, 20, 21, 22, 23, 24, 25, 26, 27.\r\n" );
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document.write( "They create 10 pairs\r\n" );
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document.write( "     (18,27), (19,26), (20,25), (21,24), (22,23), (23,22), (24,21), (25,20), (26,19), (27,18).\r\n" );
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document.write( "ANSWER.  There are 10 pairs satisfying given conditions, listed above.\r\n" );
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