document.write( "Question 1199873: The sum of the digits of a two-digit number is 11. If the digits are reversed, the new number is 45 less than the original number. Find the number.
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Algebra.Com's Answer #833849 by ikleyn(52787) $\"\"$ $\"About$

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document.write( "Let \"ab\" be the decimal presentation of the number, so \"b\" is the \"units\" digit and \"a\" is the \"tens\" digit.\r\n" );
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document.write( "Then the value of the original number is (10a+b),\r\n" );
document.write( "while the value of the reversed digit number is (10b+a).\r\n" );
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document.write( "From the problem,\r\n" );
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document.write( "    a + b = 11,                (1)\r\n" );
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document.write( "    10a + b = 10b + a + 45.    (2)\r\n" );
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document.write( "Simplify equation (2) step by step\r\n" );
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document.write( "    10a + b - 10b - a = 45\r\n" );
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document.write( "      9a - 9b = 45\r\n" );
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document.write( "      9(a-b) = 45\r\n" );
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document.write( "        a - b = 45.\r\n" );
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document.write( "Thus we have this system of equations\r\n" );
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document.write( "    a + b = 11,    (3)\r\n" );
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document.write( "    a - b =  5.    (4)\r\n" );
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document.write( "To solve the system, add equations (3) and (4)\r\n" );
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document.write( "    2a = 11 + 5 = 16,  a = 16/2 = 8.\r\n" );
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document.write( "Then from (3)  b = 11 -a = 11 - 8 = 3.\r\n" );
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document.write( "ANSWER.  The number is  83.\r\n" );
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document.write( "CHECK.  The sum of the digits is 8 + 3 = 11;\r\n" );
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document.write( "        the difference of the numbers is  83 - 38 = 45.   ! correct !\r\n" );
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