document.write( "Question 1150396: The sum of the digits of a two digit counting number is 15 , when the digits are reversed the number is 27 more than the original number . what was the original number? \n" ); document.write( "

Algebra.Com's Answer #771785 by ikleyn(52780) $\"\"$ $\"About$

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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( "The sum of the digits \"a\" and \"b\" is 15\r\n" );
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document.write( "    a + b = 15.          (3)\r\n" );
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document.write( "According to the condition, the reversed number is 27 more than the original number.  It means\r\n" );
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document.write( "    (10b+a) - (10a+b) = 27,    or\r\n" );
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document.write( "    9b - 9a = 27,\r\n" );
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document.write( "    9*(b-a) = 27,\r\n" );
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document.write( "    b-a     = 27/9 = 3.    (4)\r\n" );
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document.write( "Thus we have the system of two equations\r\n" );
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document.write( "    b + a = 15             (3')\r\n" );
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document.write( "    b - a =  3             (4')\r\n" );
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document.write( "To solve it, from equation (3') express a = 15-b  and express it into equation (4').  You will get then\r\n" );
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document.write( "    b - (15-b) = 3\r\n" );
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document.write( "    2b = 3+15 = 18,\r\n" );
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document.write( "    b = 18/2 = 9.\r\n" );
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document.write( "Then from equation (1'),  a = 15-9 = 6.\r\n" );
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document.write( "Thus the number is  69.\r\n" );
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document.write( "CHECK.  The reversed number MINUS the original number is  96 - 69 = 27.   ! Correct !\r\n" );
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