document.write( "Question 397250: the sum of the digits of a two-digit number is 17. When the digits are reversed, the new number is 9 more than the original number. What is the original number? \n" ); document.write( "
Algebra.Com's Answer #281662 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
let x = the 10's digit
\n" ); document.write( "let y = the units
\n" ); document.write( "then
\n" ); document.write( "10x + y = the original two digit number
\n" ); document.write( "and
\n" ); document.write( "10y + x = the two digit number reversed
\n" ); document.write( ":
\n" ); document.write( "the sum of the digits of a two-digit number is 17.
\n" ); document.write( "x + y = 17
\n" ); document.write( ":
\n" ); document.write( "When the digits are reversed, the new number is 9 more than the original number.
\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 by 9
\n" ); document.write( "y = x + 1
\n" ); document.write( ":
\n" ); document.write( "Replace y with (x+1) in the 1st equation
\n" ); document.write( "x + x+1 = 17
\n" ); document.write( "2x = 17-1
\n" ); document.write( "2x = 16
\n" ); document.write( "x = 8
\n" ); document.write( "then, obviously, y = 9
\n" ); document.write( ":
\n" ); document.write( "What is the original number? 89
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Confirm this in the statement:
\n" ); document.write( "\"When the digits are reversed, the new number is 9 more than the original\"
\n" ); document.write( "98 = 89 + 9 \n" ); document.write( "
\n" );