document.write( "Question 306765: The sum of the digits of a two digit counting number is 10. If the digits are reversed, the new number is two less than three times the original number. What is the original number? \n" ); document.write( "
Algebra.Com's Answer #219552 by dabanfield(803)\"\" \"About 
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The sum of the digits of a two digit counting number is 10. If the digits are reversed, the new number is two less than three times the original number. What is the original number?\r
\n" ); document.write( "\n" ); document.write( "Let x be the tens digit and y the units digit.\r
\n" ); document.write( "\n" ); document.write( "The original number then is 10*x + y. The new number is 10*y + x. \r
\n" ); document.write( "\n" ); document.write( "We have then:\r
\n" ); document.write( "\n" ); document.write( "1.) x + y = 10 and
\n" ); document.write( "2.) 3*(10*x + y) - 2 = 10*y + x\r
\n" ); document.write( "\n" ); document.write( "From 1.) we have x = 10 - y. Substituting 10 - y for x in 2.) we have:\r
\n" ); document.write( "\n" ); document.write( "3*(10*(10-y) + y) - 2 = 10*y + (10 - y)\r
\n" ); document.write( "\n" ); document.write( "3*(100 - 10y + y) - 2 = 10*y + (10 - y)
\n" ); document.write( "3*(100 - 9*y) - 2 = 10*y + (10 - y)
\n" ); document.write( "300 - 27*y - 2 = 10*y + 10 - y
\n" ); document.write( "298 - 27*y = 9*y + 10
\n" ); document.write( "36*y = 288
\n" ); document.write( "y = 8\r
\n" ); document.write( "\n" ); document.write( "Substituting 8 for y in 1.) above we have:\r
\n" ); document.write( "\n" ); document.write( "x + y = 10
\n" ); document.write( "x + 8 = 10
\n" ); document.write( "x = 2\r
\n" ); document.write( "\n" ); document.write( "The original number then is 28.\r
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