document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=843199>Question 843199</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the largest two digit integer that is increased by 75% when it's digits are reversed.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #507995 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=507995\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let your digits be a and b.\r<BR>\n" );
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document.write( "your first number is ab.<BR>\n" );
document.write( "your second number is ba.\r<BR>\n" );
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document.write( "the value of your first number is 10a + b<BR>\n" );
document.write( "the value of your second number is 10b + a.\r<BR>\n" );
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document.write( "assume that your second number is 75% bigger than your first number.\r<BR>\n" );
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document.write( "this means that your second number is 1.75 times as big as your first number.\r<BR>\n" );
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document.write( "since the value of your first number is 10a + b and the value of your second number is 10b + a, this means that:\r<BR>\n" );
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document.write( "10b + a is equal to 1.75 * (10a + b)\r<BR>\n" );
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document.write( "simplify this equation to get:\r<BR>\n" );
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document.write( "10b + a = 17.5 * a + 1.75 * b\r<BR>\n" );
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document.write( "subtract 1.75 * b from both sides of this equation and subtract a from both sides of this equation to get:\r<BR>\n" );
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document.write( "10b - 1.75b = 17.5a - a\r<BR>\n" );
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document.write( "simplify this to get:\r<BR>\n" );
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document.write( "8.25b = 16.5a\r<BR>\n" );
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document.write( "divide both sides of this equation by 8.5 to get:\r<BR>\n" );
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document.write( "b = 16.5a/8.25\r<BR>\n" );
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document.write( "this simplifies to b = 2a\r<BR>\n" );
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document.write( "since b has to be an integer, and b has to be 2a, then the biggest that b can be is 8.\r<BR>\n" );
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document.write( "if it were 9, than a would not be an integer.\r<BR>\n" );
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document.write( "it can't be 10 since a single digit can only go up to 9.\r<BR>\n" );
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document.write( "so the biggest that b can be is 8 and this means that the biggest that a can be is 4 which is 1/2 * b.\r<BR>\n" );
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document.write( "since your first number is ab, then that number is 48.<BR>\n" );
document.write( "since your second number is ba, then that number is 84.\r<BR>\n" );
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document.write( "84 is 1.75 * 48 so the solution is good.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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