document.write( "Question 82511: The sum of the digits of a two-digit number is 10. If the digits are reversed,the new number is one less than twice the original number. What is the number? \n" ); document.write( "
Algebra.Com's Answer #59110 by stanbon(75887)\"\" \"About 
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The sum of the digits of a two-digit number is 10. If the digits are reversed,the new number is one less than twice the original number. What is the number?
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\n" ); document.write( "Comment: Any two-digit number can be expressed as 10t+u where
\n" ); document.write( "t is the ten's digit and u is the unit's digit.
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\n" ); document.write( "EQUATION;
\n" ); document.write( "t+u = 10
\n" ); document.write( "10u+t = 2(10t+u)-1
\n" ); document.write( "Simplify the 2nd equation as follows:
\n" ); document.write( "10u+t = 20t+2u-1
\n" ); document.write( "19t-8u=1
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\n" ); document.write( "Rewrite as follows:
\n" ); document.write( "t+u=10
\n" ); document.write( "19t-8u=1
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\n" ); document.write( "t=10-u
\n" ); document.write( "Substitute into the 2nd equation to solve for u, as follows:
\n" ); document.write( "19(10-u)-8u=1
\n" ); document.write( "190-27u=1
\n" ); document.write( "27u=189
\n" ); document.write( "u=7
\n" ); document.write( "Then t=10-u=3
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\n" ); document.write( "The original number is 37
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
\n" ); document.write( ":\r
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