document.write( "Question 834553: the sum of the digits of a two digit number is 8. if 8 is subtracted from the number the digits interchange their places.find the number. \n" ); document.write( "
Algebra.Com's Answer #503171 by ankor@dixie-net.com(22740)\"\" \"About 
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Let a = the 10's digit
\n" ); document.write( "Let b = the units
\n" ); document.write( "then
\n" ); document.write( "10a+b = \"the number\"
\n" ); document.write( ":
\n" ); document.write( "There is no integer solutions from the way this is written,
\n" ); document.write( "Change 8 to 9 and it works
\n" ); document.write( ":
\n" ); document.write( " the sum of the digits of a two digit number is 9.
\n" ); document.write( "a + b = 9
\n" ); document.write( "a = (9-b); use this form for substitution
\n" ); document.write( ":
\n" ); document.write( "if 9 is subtracted from the number, the digits interchange their places.
\n" ); document.write( "10a + b - 9 = 10b + a
\n" ); document.write( "10a - a = 10b - b + 9
\n" ); document.write( "9a = 9b + 9
\n" ); document.write( "simplify, divide by 9
\n" ); document.write( "a = b + 1
\n" ); document.write( "replace a with (9-b)
\n" ); document.write( "9 - b = b + 1
\n" ); document.write( "9 - 1 = b + b
\n" ); document.write( "8 = 2b
\n" ); document.write( "b = 4
\n" ); document.write( "then
\n" ); document.write( "a = 5
\n" ); document.write( "find the number. 54
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check
\n" ); document.write( "54 - 9 = 45 \n" ); document.write( "
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