document.write( "Question 1163432: In a two digit number the tens digit is 3 more than the ones digit. If the digits are reversed the difference between the two numbers is 27. Find the number. \r
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Algebra.Com's Answer #787517 by ikleyn(52799) $\"\"$ $\"About$

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\n" ); document.write( "In a two digit number the tens digit is 3 more than the ones digit. If the digits are reversed
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document.write( "Let \"a\" be the tens digit of the 2-digit number, and\r\n" );
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document.write( "let \"b\" be the ones digit of the number.\r\n" );
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document.write( "Then the number is\r\n" );
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document.write( "    n = 10a + b,         (1)\r\n" );
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document.write( "while the reversed digit number is \r\n" );
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document.write( "    m = 10b + a.         (2)\r\n" );
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document.write( "Since the tens digit is 3 more than the ones, the original number is greater than the reversed one. \r\n" );
document.write( "Hence, according to the condition, the original number is 27 more than the reversed number.  It means\r\n" );
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document.write( "    (10a+b) - (10b+a) = 27,    or\r\n" );
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document.write( "    9a - 9b = 27,\r\n" );
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document.write( "    9*(a-b) = 27,\r\n" );
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document.write( "    a-b     = 27/9 = 3.    (3)\r\n" );
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document.write( "Notice that it is exactly the FIRST condition given in the problem.\r\n" );
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document.write( "Thus in the problem the first condition IS NOT INDEPENDENT: it is just contained in the second condition.\r\n" );
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document.write( "Surely, it is the problem's FAULT, which leads to the fact that the final solution is not unique.\r\n" );
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document.write( "Any of the numbers  41, 52, 63, 74, 85, 96  satisfies the problem's condition.      ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Today I observe a FLOW of problems, part of which have curved formulation, while another part are simply INCORRECT.\r
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\n" ); document.write( "\n" ); document.write( "It becomes really interesting to me, who creates these heavily sick problems and from which GARBAGE BOX the visitors recover them.\r
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\n" ); document.write( "\n" ); document.write( "Probably, the time came to issue this WARNING:\r
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\n" ); document.write( "\n" ); document.write( "If I will see the flow of nonsensical or heavy sick problems, I will collect their links\r
\n" ); document.write( "\n" ); document.write( "and write to the MANAGERS of this project asking them take PERSONAL measures against such visitors.\r
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