document.write( "Question 697600: If the digits of a two-digit number are interchanged, the result exceeds the original number by 2 more than the sum of the digits. The digits differ by 2. Find the original number. \n" ); document.write( "

Algebra.Com's Answer #430160 by Edwin McCravy(20060) $\"\"$ $\"About$

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If the digits of a two-digit number, 10t+u,
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document.write( "That's 10u+t\r\n" );
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\n" ); document.write( "the result exceeds the original number
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document.write( "That means 10u+t = 10t+u PLUS something\r\n" );
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document.write( "Now we're about hear what we are supposed to PLUS onto that\r\n" );
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document.write( "Well, the sum of the digits is t+u, and 2 more\r\n" );
document.write( "than that is t+u+2.\r\n" );
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document.write( "So we have that 10u+t = 10t+u PLUS t+u+2\r\n" );
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document.write( "or\r\n" );
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document.write( "10u+t = 10t+u + t+u+2\r\n" );
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document.write( "simplify:\r\n" );
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document.write( "10u+t = 11t+2u+2\r\n" );
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document.write( "   8u = 10t+2\r\n" );
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document.write( "Divide through by 2\r\n" );
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document.write( "   4u = 5t+1\r\n" );
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document.write( "The digits differ by 2.  
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document.write( "Oh oh! That doesn't tell us which way to subtract them.\r\n" );
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document.write( "It could be t-u = 2 or u-t = 2\r\n" );
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document.write( "So we have two possible systems of equations:\r\n" );
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document.write( "or\r\n" );
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document.write( "Solve each one by substitution.\r\n" );
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document.write( "One of them comes out t = -9 and u = -11\r\n" );
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document.write( "But that's impossible.  The other one is t=7, u=9\r\n" );
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document.write( "So the number must be 79\r\n" );
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document.write( "Edwin
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