document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=521532>Question 521532</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When a certain three digit number is divided by the number with digits reversed, the quotient is 2 and the remainder is 25. The tens digit is one less than twice the sum of the hundreds digits and units digit. If the units digit is subtracted from the tens digit, the result is twice the hundreds digits. 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 #346567 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=346567\">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( "then<BR>\n" );
document.write( "100a + 10b + c = the number<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write an equation for each statement:<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"When a certain three digit number is divided by the number with 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%2Bc%29%2F%28100c%2B10b%2Ba%29 ALIGN=MIDDLE  ALT=\"%28100a%2B10b%2Bc%29%2F%28100c%2B10b%2Ba%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2F%28100c%2B10b%2Ba%29 ALIGN=MIDDLE  ALT=\"25%2F%28100c%2B10b%2Ba%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply thru by 100c+10b+a, results get rid of the denominators:<BR>\n" );
document.write( "100a+10b+c = 2(100c+10b+a) + 25<BR>\n" );
document.write( ":<BR>\n" );
document.write( "100a + 10b + c = 200c + 20b + 2a + 25<BR>\n" );
document.write( "Combine like terms<BR>\n" );
document.write( "100a - 2a = 200c - c + 20b - 10b + 25<BR>\n" );
document.write( ":<BR>\n" );
document.write( "98a = 199c + 10b + 25<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\" The tens digit is one less than twice the sum of the hundreds digits and units digit.\"<BR>\n" );
document.write( "b = 2(a+c) - 1<BR>\n" );
document.write( "b = 2a + 2c - 1<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\" If the units digit is subtracted from the tens digit, the result is twice the hundreds digits.\"<BR>\n" );
document.write( "b - c = 2a<BR>\n" );
document.write( "b = c + 2a<BR>\n" );
document.write( ":<BR>\n" );
document.write( "b=b, therefore<BR>\n" );
document.write( "2a + 2c - 1 = c + 2a<BR>\n" );
document.write( "Subtract 2a from both sides:<BR>\n" );
document.write( "2c - 1 = c<BR>\n" );
document.write( "2c - c = 1<BR>\n" );
document.write( "c = 1<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The 1st equation simplified<BR>\n" );
document.write( "98a = 199c + 10b + 25<BR>\n" );
document.write( "replace c with 1, in both equations<BR>\n" );
document.write( "98a = 199 + 10b + 25<BR>\n" );
document.write( "98a = 10b + 224<BR>\n" );
document.write( ":<BR>\n" );
document.write( "b = 2a + c<BR>\n" );
document.write( "b = (2a+1)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "98a = 10b + 224<BR>\n" );
document.write( "substitute for b<BR>\n" );
document.write( "98a = 10(2a+1) + 224<BR>\n" );
document.write( "98a = 20a + 10 + 224<BR>\n" );
document.write( "98a - 20a = 234<BR>\n" );
document.write( "78a = 234<BR>\n" );
document.write( "a = 234/78<BR>\n" );
document.write( "a = 3<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find b<BR>\n" );
document.write( "b = 2a + c<BR>\n" );
document.write( "b = 2(3) + 1<BR>\n" );
document.write( "b = 7<BR>\n" );
document.write( "then<BR>\n" );
document.write( "371 is the number!<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check this in the 1st statement:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=371%2F173 ALIGN=MIDDLE  ALT=\"371%2F173\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2F173 ALIGN=MIDDLE  ALT=\"25%2F173\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );