document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1035728>Question 1035728</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the digits of a two-digit number is 11. When the numbers are reversed, the new number is 20 less than twice the original. What is the original number? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #650383 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=650383\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let the 2 digits of the number be a and b.\r<BR>\n" );
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document.write( "a is the tens digit.<BR>\n" );
document.write( "b is the units digit.<BR>\n" );
document.write( "the value of the 2 digit number is 10a + b.\r<BR>\n" );
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document.write( "the sum of the digits of the 2 digit number is 11.<BR>\n" );
document.write( "this means that a + b = 11.\r<BR>\n" );
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document.write( "when the numbers are reversed, the new number is 20 less than twice the original number.\r<BR>\n" );
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document.write( "this means that 10b + a = 2 * (10a + b) - 20.\r<BR>\n" );
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document.write( "simplify this to get 10b + a = 20a + 2b - 20.<BR>\n" );
document.write( "subtract 20a and 2b from both sides of this equation to get 10b - 2b + a - 20a = -20.\r<BR>\n" );
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document.write( "simplify this to get 8b - 19a = -20.\r<BR>\n" );
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document.write( "from a + b = 11, solve for a to get a = 11 - b.<BR>\n" );
document.write( "replace a with 11 - b in the equation of 8b - 19a = -20 to get 8b - 19 * (11 - b) = -10.<BR>\n" );
document.write( "simplify this to get 8b - 209 + 19b = -20<BR>\n" );
document.write( "combine like terms to get 27b - 209 = -20<BR>\n" );
document.write( "add 209 to both sides of this equation to get 27b = 189.<BR>\n" );
document.write( "divide both sides of this equation by 27 to get b = 189/27 = 7\r<BR>\n" );
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document.write( "you have b = 7.<BR>\n" );
document.write( "since a + b = 11, this means that a = 4.\r<BR>\n" );
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document.write( "your original number is ab = 47.<BR>\n" );
document.write( "when you reverse the digits, you get ba = 74.\r<BR>\n" );
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document.write( "your original statement says that when the numbers are reversed, the new number is 20 less than twice the original.\r<BR>\n" );
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document.write( "this means that 74 is equal to 20 less than 2 * 47.<BR>\n" );
document.write( "2 * 47 = 94.<BR>\n" );
document.write( "94 - 20 = 74.<BR>\n" );
document.write( "74 is equal to 74, confirming that the solution is correct.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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