document.write( "Question 1143268: The sum of two whole number is 45. Their difference is less than 10.the number of all possible pair is \n" ); document.write( "

Algebra.Com's Answer #764208 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " The analysis and the answer by Edwin are incorect: he gives many \"solutions\", that are not the solutions at all.\r
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document.write( "Let x is the greatest of the two numbers x and y satisfying the condition.\r\n" );
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document.write( "Then\r\n" );
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document.write( "    x  + y = 45,     (1)\r\n" );
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document.write( "    x - y  < 10.     (2)\r\n" );
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document.write( "Express y = 45 - x from (1) and substitute it into (2). You will get\r\n" );
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document.write( "    x - (45-x) < 10.\r\n" );
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document.write( "    2x - 45 < 10\r\n" );
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document.write( "    2x      < 10 + 45 = 55\r\n" );
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document.write( "     x      < 55/2 = 27.5.\r\n" );
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document.write( "So, the solutions are these 5 pairs (x,y),  where y = 45-x,  x is the largest of the two numbers  and  x-y < 10 :\r\n" );
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document.write( "    (27,18), (26, 19), (25,20), (24,21), (23,22).   (*)\r\n" );
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document.write( "Five reversed pairs\r\n" );
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document.write( "    (18,27), (19,26), (20,25), (24,21), (22,23)      (**)\r\n" );
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document.write( "are the solutions to the original problem, too.\r\n" );
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document.write( "So,  10 pairs  (*)  and  (**), and only they, are the solutions to the problem. \r\n" );
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document.write( "ANSWER.  The number of all possible pairs is 10.\r\n" );
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