document.write( "Question 146922: The sum of the digits of a two-digit numeral is 8. If the digits are reversed, the new number is 18 greater than the original number. Find the original number. \n" ); document.write( "
Algebra.Com's Answer #107292 by ptaylor(2198)\"\" \"About 
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Let x=the tens digit
\n" ); document.write( "And let y=the units digit
\n" ); document.write( "The original number is 10x+y
\n" ); document.write( "If the digits are reversed, the new number is 10y+x\r
\n" ); document.write( "\n" ); document.write( "Now we are told the following:\r
\n" ); document.write( "\n" ); document.write( "x+y=8--------------------------------------eq1\r
\n" ); document.write( "\n" ); document.write( "And\r
\n" ); document.write( "\n" ); document.write( "10y+x=10x+y+18-------------------------------eq2\r
\n" ); document.write( "\n" ); document.write( "simplifying eq2, by subtracting 10x and also y from each side:
\n" ); document.write( "10y-y+x-10x=10x-10x+y-y+18 collect like terms
\n" ); document.write( "9y-9x=18 divide each term by -9
\n" ); document.write( "x-y=-2------------------------------------------------eq2a\r
\n" ); document.write( "\n" ); document.write( "Add eq1 and eq2a:\r
\n" ); document.write( "\n" ); document.write( "2x=6 divide each side by 2
\n" ); document.write( "x=3-------------------------------the 10's digit\r
\n" ); document.write( "\n" ); document.write( "Substitute x=3 into eq1:\r
\n" ); document.write( "\n" ); document.write( "3+y=8
\n" ); document.write( "y=5------------------------------the units digit\r
\n" ); document.write( "\n" ); document.write( "The original number is: 35
\n" ); document.write( "The new number is 53 which is 18 greater than 35\r
\n" ); document.write( "\n" ); document.write( "Hope this helps---ptaylor
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