document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1052913>Question 1052913</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When a certain 3-digit number is divided by the number with the digits reversed, the quotient is 2 and the remainder is 25. The tens digit is one less than twice the sum of the hundreds digit and units digit. If the units digit is subtracted from the tens digit the result is twice the hundreds digit. 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 #668246 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=668246\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let a = the 100's digit<BR>\n" );
document.write( "let b = the 10's<BR>\n" );
document.write( "let c = the units<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write an equiv equation for each statement, simplify as much as possible<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"When a certain 3-digit number is divided by the number with the digits reversed, the quotient is 2 and the remainder is 25.\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28100a%2B10b+%2B+c+-+25%29%2F%28100c+%2B+10b+%2B+a%29+=+2 ALIGN=MIDDLE  ALT=\"%28100a%2B10b+%2B+c+-+25%29%2F%28100c+%2B+10b+%2B+a%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply by (100c+10b+a) and you have<BR>\n" );
document.write( "100a + 10b + c - 25 = 2(100c + 10b + a)<BR>\n" );
document.write( "100a + 10b + c - 25 = 200c + 20b + 2a  <BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"The tens digit is one less than twice the sum of the hundreds digit and units digit.\"<BR>\n" );
document.write( "b = 2(a+c) - 1<BR>\n" );
document.write( "b = 2a + 2c - 1<BR>\n" );
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document.write( "\"If the units digit is subtracted from the tens digit the result is twice the hundreds digit. \"<BR>\n" );
document.write( "b - c = 2a<BR>\n" );
document.write( "In the 2nd equation, replace 2a with(b-c)<BR>\n" );
document.write( "b = (b-c) + 2c - 1<BR>\n" );
document.write( "b - b = 2c - c - 1<BR>\n" );
document.write( "0 = c - 1<BR>\n" );
document.write( "therefore<BR>\n" );
document.write( "c = 1<BR>\n" );
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document.write( "Using the 1st equation simplified, replace c with 1<BR>\n" );
document.write( "100a + 10b + 1 - 25 = 200(1) + 20b + 2a  <BR>\n" );
document.write( "100a - 2a + 10b - 20b - 24  = 200<BR>\n" );
document.write( "98a - 10b = 200 + 24<BR>\n" );
document.write( "98a - 10b = 224<BR>\n" );
document.write( "Simplify, divide by 2<BR>\n" );
document.write( "49a - 5b = 112<BR>\n" );
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document.write( "In the 2nd equation, simplified, replace c with 1<BR>\n" );
document.write( "b = 2a +2(1) - 1<BR>\n" );
document.write( "-2a + b = 1<BR>\n" );
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document.write( "Use elimination, multiply the above equation by 5 add<BR>\n" );
document.write( "49a - 5b = 112<BR>\n" );
document.write( "-10a+ 5b =  5<BR>\n" );
document.write( "-------------------Adding eliminates b, find a<BR>\n" );
document.write( "39a = 117<BR>\n" );
document.write( "a = 117/39<BR>\n" );
document.write( "a = 3<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find b<BR>\n" );
document.write( "we know b = 2a + 2c -1<BR>\n" );
document.write( "replace a and c<BR>\n" );
document.write( "b = 2(3) + 2(1) = 1<BR>\n" );
document.write( "b = 6 + 2 - 1<BR>\n" );
document.write( "b = 7<BR>\n" );
document.write( "Therefore<BR>\n" );
document.write( "our number = 371<BR>\n" );
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document.write( ";<BR>\n" );
document.write( "Check this in the first statement<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28371-25%29%2F173 ALIGN=MIDDLE  ALT=\"%28371-25%29%2F173\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=346%2F173 ALIGN=MIDDLE  ALT=\"346%2F173\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2<BR>\n" );
document.write( "You can check them in the other two statments<BR>\n" );
document.write( " </SPAN>\n" );
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