document.write( "Question 687054: in a two digit number two times the ten digit is eight less than seven times the one\"s digit.when the digits are interchanged, it reduces by nine.find the number? \n" ); document.write( "
Algebra.Com's Answer #425035 by ankor@dixie-net.com(22740)\"\" \"About 
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let x = the 10's digit
\n" ); document.write( "let y = the one's digit
\n" ); document.write( "then
\n" ); document.write( "10x+y = the number
\n" ); document.write( ":
\n" ); document.write( "in a two digit number two times the ten digit is eight less than seven times the one\"s digit.
\n" ); document.write( "2x = 7y - 8
\n" ); document.write( "2x - 7y = -8
\n" ); document.write( ":
\n" ); document.write( "when the digits are interchanged, it reduces by nine.
\n" ); document.write( "10y + x = 10x + y - 9
\n" ); document.write( "10y - y + x - 10x = -9
\n" ); document.write( "9y - 9x = -9
\n" ); document.write( "Divide by -9
\n" ); document.write( "x - y = 1
\n" ); document.write( "x = y + 1
\n" ); document.write( ":
\n" ); document.write( "In the 1st equation replace x with (y+1)
\n" ); document.write( "2(y+1) - 7y = -8
\n" ); document.write( "2y + 2 - 7y = -8
\n" ); document.write( "-5y = -8 - 2
\n" ); document.write( "-5y = -10
\n" ); document.write( "y = +2
\n" ); document.write( ":
\n" ); document.write( "Find x using x = y + 1
\n" ); document.write( "x = 2 + 1
\n" ); document.write( "x = 3
\n" ); document.write( "therefore
\n" ); document.write( "32 is the number
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check this in the statement:
\n" ); document.write( "\"when the digits are interchanged, it reduces by nine\"
\n" ); document.write( "23 = 32 - 9\r
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