document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=970206>Question 970206</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the middle digit of a three digit number is half the sum of the other two digits. The number is 20.5 times the sum of its digits. The new number obtained by interchanging the digits in the unit's and hundred's places is more than the original number by 594. Find 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 #592880 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=592880\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let a = 100's digit<BR>\n" );
document.write( "let b = the 10's<BR>\n" );
document.write( "let c = the units<BR>\n" );
document.write( "then<BR>\n" );
document.write( "100a+10b+c = the original number<BR>\n" );
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document.write( "Write an equation for each statement, simplify as much as possible<BR>\n" );
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document.write( " the middle digit of a three digit number is half the sum of the other two digits.<BR>\n" );
document.write( "b = .5(a+c)<BR>\n" );
document.write( "b = .5a + .5c<BR>\n" );
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document.write( " The number is 20.5 times the sum of its digits.<BR>\n" );
document.write( "100a+10b+c = 20.5(a+b+c)<BR>\n" );
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document.write( " The new number obtained by interchanging the digits in the unit's and hundred's places is more than the original number by 594.<BR>\n" );
document.write( "100a + 10b + c + 594 = 100c + 10b + a<BR>\n" );
document.write( "100a - a + 10b - 10b = 100c - c - 594<BR>\n" );
document.write( "99a = 99c - 594<BR>\n" );
document.write( "simplify, divide by 99<BR>\n" );
document.write( "a = c - 6<BR>\n" );
document.write( "We know that c has to be 7, 8, or 9<BR>\n" );
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document.write( "in the first equation, b = .5a + .5c, replace a with (c+6)<BR>\n" );
document.write( "b = .5(c-6) + .5c<BR>\n" );
document.write( "b = .5c - 3 + .5c<BR>\n" );
document.write( "b = c - 3<BR>\n" );
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document.write( "If c = 9, then the number is 369<BR>\n" );
document.write( "if c = 8, then the number is 258<BR>\n" );
document.write( "if c = 7, then the number is 147<BR>\n" );
document.write( "All of these numbers, when reversed, have a difference is 594?<BR>\n" );
document.write( "Which of these satisfy the 2nd statement<BR>\n" );
document.write( "369/18 = 20.5<BR>\n" );
document.write( "258/15 = 17.2<BR>\n" );
document.write( "147/12 = 12.25\r<BR>\n" );
document.write( "\n" );
document.write( " Find the original number 369 </SPAN>\n" );
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