document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1166205>Question 1166205</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the digits in a certain three digit number is 11. The difference of the first and the third digits is one less than the middle digit. If the hundreds and tens digits are interchanged, the number is reduced by 90. Find the number. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #790696 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=790696\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "I didn't look closely at the solution by the other tutor.  There are many ways to solve the problem using formal algebra; that solution shows one of them.<br><BR>\n" );
document.write( "If a formal algebraic solution is not required, a bit of logical reasoning and some simple mental arithmetic will find the answer quickly.<br><BR>\n" );
document.write( "Logical analysis should easily show that, since switching the hundreds and tens digit reduces the number by 90, the hundreds digit is 1 more than the tens digit.<br><BR>\n" );
document.write( "Then the requirement that the sum of the digits be 11 leaves only a very few possibilities for the number:<BR>\n" );
document.write( "218<BR>\n" );
document.write( "326<BR>\n" );
document.write( "434<BR>\n" );
document.write( "542<BR>\n" );
document.write( "650<br><BR>\n" );
document.write( "In only one of those numbers is the other requirement satisfied -- that the difference between the first and third digits is one less than the middle digit: 542.<br><BR>\n" );
document.write( "ANSWER: 542<br><BR>\n" );
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