document.write( "Question 140535: When the digits of a two-digit number are reversed, the new number is 9 more than the original number, and the sum of the digits of the original number is 11. What is the original number? \n" ); document.write( "
Algebra.Com's Answer #102324 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
When the digits of a two-digit number are reversed, the new number is 9 more than the original number, and the sum of the digits of the original number is 11. What is the original number?
\n" ); document.write( ":
\n" ); document.write( "Let x = the 10's digit
\n" ); document.write( "Let y = the units digit (original number)
\n" ); document.write( ":
\n" ); document.write( "write an equation for the statement:
\n" ); document.write( "\"When the digits of a two-digit number are reversed, the new number is 9 more than the original number,\"
\n" ); document.write( ":
\n" ); document.write( "10y + x = (10x + y) + 9
\n" ); document.write( "10y - y = 10x - x + 9
\n" ); document.write( "9y = 9x + 9
\n" ); document.write( "simplify, divide equation by 9
\n" ); document.write( "y = x + 1
\n" ); document.write( ":
\n" ); document.write( "\"the sum of the digits of the original number is 11.\"
\n" ); document.write( "x + y = 11
\n" ); document.write( "Substitute (x+1) for y
\n" ); document.write( "x + (x+1) = 11
\n" ); document.write( "2x = 11 - 1
\n" ); document.write( "x = \"10%2F2\"
\n" ); document.write( "x = 5, then y = 6
\n" ); document.write( ":
\n" ); document.write( "What is the original number?
\n" ); document.write( "56
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check:
\n" ); document.write( "65 = 56 + 9\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );