document.write( "Question 1197732: 2) The sum of the digits of a two- digit counting number is 6. When the digits are reversed, the number is 18 greater than the original number. What was the original number? \n" ); document.write( "

Algebra.Com's Answer #831120 by ikleyn(52832) $\"\"$ $\"About$

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\n" ); document.write( "The sum of the digits of a two- digit counting number is 6.
\n" ); document.write( "When the digits are reversed, the number is 18 greater than the original number.
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document.write( "Let the digits of the original number be \"a\" and \"b\", reading from left to right.\r\n" );
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document.write( "Then the number is 10a+b,  and we are given thast \r\n" );
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document.write( "    a + b = 6.    (1)\r\n" );
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document.write( "The reversed number in written form is  \"ba\" :  its value is  10b+a.\r\n" );
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document.write( "So, we have second equation\r\n" );
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document.write( "    (10b+a) - (10a+b) = 18,\r\n" );
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document.write( "or\r\n" );
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document.write( "    9b - 9a = 18\r\n" );
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document.write( "    9(b-a)  = 18\r\n" );
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document.write( "     b - a  = 2.    (2)\r\n" );
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document.write( "Thus you have two equations, (1) and (2), to find \"a\" and \"b\".\r\n" );
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document.write( "To do it, express  b = 6-a  from (1) and substitute into (2).  You will get\r\n" );
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document.write( "    (6-a) - a = 2\r\n" );
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document.write( "     6 - 2a   = 2\r\n" );
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document.write( "     6 - 2    = 2a\r\n" );
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document.write( "       4      = 2a\r\n" );
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document.write( "       a      = 4/2 = 2.\r\n" );
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document.write( "Thus you found  a= 2,  b= 6-a = 6-2= 4.\r\n" );
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document.write( "Hence, the original number is  24.    ANSWER\r\n" );
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