document.write( "Question 82606: The sum of the digits of a two-digit counting number was 11. When the digits were reversed, the new number was 10 more than one-half the original number. What was the original number? \n" ); document.write( "
Algebra.Com's Answer #59200 by ankor@dixie-net.com(22740)\"\" \"About 
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Let x = the 10's digit; let y = the units digit
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\n" ); document.write( "\"The sum of the digits of a two-digit counting number was 11.\"
\n" ); document.write( " x + y = 11
\n" ); document.write( "or x = (11 - y)
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\n" ); document.write( "\"When the digits were reversed, the new number was 10 more than one-half the original number.\"
\n" ); document.write( " 10y + x = .5(10x + y) + 10
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\n" ); document.write( "What was the original number?
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\n" ); document.write( "10y + x = .5(10x + y) + 10
\n" ); document.write( "10y + x = 5x + .5y + 10
\n" ); document.write( "10y -.5y = 5x - x + 10
\n" ); document.write( "9.5y = 4x + 10\r
\n" ); document.write( "\n" ); document.write( "replace x with (11-y)
\n" ); document.write( "9.5y = 4(11-y) + 10
\n" ); document.write( "9.5y = 44 - 4y + 10
\n" ); document.write( "9.5y + 4y = 54
\n" ); document.write( "13.5y = 54
\n" ); document.write( "y = 54/13.5
\n" ); document.write( "y = 4
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\n" ); document.write( "find x:
\n" ); document.write( "x = 11-y
\n" ); document.write( "x = 11-4
\n" ); document.write( "x = 7
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\n" ); document.write( "The number: 74
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\n" ); document.write( "Check using:
\n" ); document.write( "\"When the digits were reversed, the new number was 10 more than one-half the original number.\"
\n" ); document.write( " 47 = .5(74) + 10
\n" ); document.write( " 47 = 37 + 10
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