document.write( "Question 1143565: The sum of two whole number is 45 and their difference is less than 10. The number of all possible pair is \n" ); document.write( "

Algebra.Com's Answer #764398 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "The sum of two whole number is 45 and their difference is less than 10. The number of all possible $\"highlight%28cross%28pair%29%29\"$ pairs is
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document.write( "x + y = 45,   (1)\r\n" );
document.write( "x - y < 10.   (2)   (where x is the larger number)\r\n" );
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document.write( "Express x from (1): x = 45 - y,  and substitute it into (2). You will get\r\n" );
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document.write( "45 - y - y < 10,  or\r\n" );
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document.write( "45 - 2y < 10,  or\r\n" );
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document.write( "2y > 45 - 10,  or\r\n" );
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document.write( "y > (45 - 10)/2.\r\n" );
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document.write( "Hence, y > 17. Then x < 10 + 17 = 27. (And  x > y).\r\n" );
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document.write( "Answer.  These 5 pairs         (27,18), (26,19), (25,20), (24,21), (23,22) \r\n" );
document.write( "         and 5 reversed pairs  (18,27), (19,26), (20,25), (21,24), (22,23)  is the full list of solutions.\r\n" );
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document.write( "         In all, there are 10 different pairs of solutions, listed above.\r\n" );
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