document.write( "Question 68268This question is from textbook An Incremental Development
\n" ); document.write( ": The sum of the digits of a two-digit counting number was 9. When the digits were reversed, the new number was 45 less than the original number. What was the original number? \n" ); document.write( "
Algebra.Com's Answer #48562 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "Let x = the 1st digit; y = 2nd digit
\n" ); document.write( ":
\n" ); document.write( "\"The sum of the digits of a two-digit counting number was 9.\"
\n" ); document.write( "x + y = 9
\n" ); document.write( "x = (9 - y)
\n" ); document.write( ":
\n" ); document.write( "original number: 10x + y
\n" ); document.write( "Reversed number: 10y + x
\n" ); document.write( ":
\n" ); document.write( "\"the digits were reversed, the new number was 45 less than the original number\"
\n" ); document.write( "(10y + x) + 45 = 10x + y
\n" ); document.write( ":
\n" ); document.write( "Perform operations to get variables on the left and number on the right
\n" ); document.write( "10y - y + x - 10x = -45
\n" ); document.write( "9y - 9x = -45
\n" ); document.write( ":
\n" ); document.write( "Simplify divide equation by 9:
\n" ); document.write( "y - x = -5
\n" ); document.write( ":
\n" ); document.write( "Substitute (9-y) for x:
\n" ); document.write( "y - (9-y) = -5
\n" ); document.write( "y - 9 + y = -5
\n" ); document.write( "2y = -5 + 9
\n" ); document.write( "2y = +4
\n" ); document.write( "y = 2
\n" ); document.write( ":
\n" ); document.write( "Find x: 9 - 2 = 7
\n" ); document.write( ":
\n" ); document.write( "Original number 72, reversed number 27
\n" ); document.write( ":
\n" ); document.write( "Check: 72 - 27 = 45\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );