document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1103484>Question 1103484</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A three digit number is equal to 17times sum of its digit. If 198 is added to the number the extreme digit get interchanged. The sum of the first and third digit is 1 less than the middle term. 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 #718227 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=718227\">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 tens<BR>\n" );
document.write( "let c = the units<BR>\n" );
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document.write( "Write an equation for each statement, simplify as much as you can<BR>\n" );
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document.write( "A three digit number is equal to 17 times sum of its digit.<BR>\n" );
document.write( "100a + 10b + c = 17(a+b+c)<BR>\n" );
document.write( "100a + 10b + c = 17a + 17b + 17c<BR>\n" );
document.write( "100a - 17a + 10b - 17b + c - 17c = 0<BR>\n" );
document.write( "83a - 7b - 16c = 0<BR>\n" );
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document.write( " If 198 is added to the number the extreme digit get interchanged.<BR>\n" );
document.write( "100a + 10b + c + 198 = 100c + 10b + a<BR>\n" );
document.write( "100a - a + 10b - 10b +c - 100c = -198<BR>\n" );
document.write( "99a - 99c = -198<BR>\n" );
document.write( "simply divide by 99<BR>\n" );
document.write( "a - c = -2<BR>\n" );
document.write( "Rearrange<BR>\n" );
document.write( "c = a + 2<BR>\n" );
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document.write( " The sum of the first and third digit is 1 less than the middle term. <BR>\n" );
document.write( "a + c = b - 1<BR>\n" );
document.write( "a - b + c = -1<BR>\n" );
document.write( "Using these two equations<BR>\n" );
document.write( "a - b + c = -1<BR>\n" );
document.write( "a + 0 - c = -2<BR>\n" );
document.write( "----------------Adding eliminates c<BR>\n" );
document.write( "2a - b + 0 = -3<BR>\n" );
document.write( "2a - b = -3<BR>\n" );
document.write( "Rearrange<BR>\n" );
document.write( "b = 2a + 3<BR>\n" );
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document.write( "Using the 1st simplified equation: 83a - 7b - 16c = 0<BR>\n" );
document.write( "replace a with (2a+3); replace c with (a+2)<BR>\n" );
document.write( "83a - 7(2a+3) - 16(a+2) = 0<BR>\n" );
document.write( "83a - 14a - 21 - 16c - 32 = 0<BR>\n" );
document.write( "83a - 30a - 53 = 0<BR>\n" );
document.write( "53a = 53<BR>\n" );
document.write( "a = 1<BR>\n" );
document.write( "then<BR>\n" );
document.write( "b = 2(1) + 3<BR>\n" );
document.write( "b = 5<BR>\n" );
document.write( "and<BR>\n" );
document.write( "c = 1 + 2<BR>\n" );
document.write( "c = 3<BR>\n" );
document.write( "Find the number. 153 is the number<BR>\n" );
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document.write( "Check this in the first statement<BR>\n" );
document.write( "\"A three digit number is equal to 17 times sum of its digit.<BR>\n" );
document.write( "153 = 17(1+5+3)<BR>\n" );
document.write( "153 = 17(9)<BR>\n" );
document.write( " </SPAN>\n" );
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