document.write( "Question 1169939: Good day. May you please assist me in the following question:\r
\n" ); document.write( "\n" ); document.write( "Consider the integers x and y. When y is divided by x the remainder is 29. When y is divided by x/2, the remainder is 13. Determine x.\r
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Algebra.Com's Answer #794852 by ikleyn(52810) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "Consider $\"highlight%28cross%28the%29%29\"$ positive integer numbers x and y.
\n" ); document.write( "When y is divided by x the remainder is 29. When y is divided by x/2, the remainder is 13. Determine x.
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\n" ); document.write( "\n" ); document.write( "            You just saw the solutions by other tutors suggesting to use trial and error method.\r
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\n" ); document.write( "\n" ); document.write( "            Meanwhile, the problem admits simple straightforward pure mathematical solution based on reasoning, ONLY.\r
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\n" ); document.write( "\n" ); document.write( "            In my opinion, it is the most suitable solution for this problem.\r
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\n" ); document.write( "\n" ); document.write( "            And I am 179% sure that this solution is what you are seeking for.\r
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document.write( "(1)  Consider the statement \"When y is divided by x the remainder is 29\".\r\n" );
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document.write( "     It means that there is an integer number \"n\" such that\r\n" );
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document.write( "        y = nx + 29,   29 < x.         (1)\r\n" );
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document.write( "(2)  Consider next statement \"When y is divided by x/2, the remainder is 13\".\r\n" );
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document.write( "     It means that there is an integer number \"m\" such that\r\n" );
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document.write( "        y = ,   13 < .     (2)\r\n" );
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document.write( "(3)  From equations (1) and (2)  we have\r\n" );
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document.write( "        nx + 29 = ,    x > 29   \r\n" );
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document.write( "     or, equivalently\r\n" );
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document.write( "        2nx + 58 = mx + 26,     x > 29\r\n" );
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document.write( "        58 - 26  = mx - 2nx,    x > 29\r\n" );
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document.write( "        32       = (m - 2n)x,   x > 29      (3)\r\n" );
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document.write( "(4)  Thus, the integer number  x  is a divisor of the number 32, and x > 29.\r\n" );
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document.write( "     But the only such integer is  x = 32.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The problem is just solved, and the ANSWER is: the number \" x \" is 32.\r
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