document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=986202>Question 986202</A>: <I><SPAN STYLE=\"word-break: break-all;\"> twice the middle digit of a three- digit number is the sum of the other two. if the no. is divided by the sum of its digit, the answer is 56 and the remainder is 8. If the digits are reversed, the number becomes smaller by 594. Find the no. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #607409 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=607409\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Spent a lot of time on this problem, unable to get integer solution when the remainder is 8, changing the remainder to 12 will solve it\r<BR>\n" );
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document.write( "let a = the 100's digit<BR>\n" );
document.write( "let b = the 10's digit<BR>\n" );
document.write( "let c = the units<BR>\n" );
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document.write( "Write an equation for each statement<BR>\n" );
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document.write( "twice the middle digit of a three-digit number is the sum of the other two.<BR>\n" );
document.write( "2b = a + c<BR>\n" );
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document.write( " if the no. is divided by the sum of its digit, the answer is 56 and the remainder is 12.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28100a%2B10b%2Bc-12%29%29%2F%28%28a%2Bb%2Bc%29%29 ALIGN=MIDDLE  ALT=\"%28%28100a%2B10b%2Bc-12%29%29%2F%28%28a%2Bb%2Bc%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 56<BR>\n" );
document.write( "here we can replace a+c with 2b from the 1st statement, so we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28100a%2B10b%2Bc-12%29%29%2F%283b%29 ALIGN=MIDDLE  ALT=\"%28%28100a%2B10b%2Bc-12%29%29%2F%283b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 56<BR>\n" );
document.write( "100a + 10b + c - 12 = 56(3b)<BR>\n" );
document.write( "100a + c = 168b - 10b + 12<BR>\n" );
document.write( "100a + c = 158b + 12<BR>\n" );
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document.write( " If the digits are reversed, the number becomes smaller by 594.<BR>\n" );
document.write( "100c + 10b + a = 100a + 10b + c - 594<BR>\n" );
document.write( "Combine like terms<BR>\n" );
document.write( "100c - c + 10b - 10b = 100a - a - 594<BR>\n" );
document.write( "99c = 99a - 594<BR>\n" );
document.write( "simplify divide by 99<BR>\n" );
document.write( "c = a - 6<BR>\n" );
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document.write( "Back to the first equation 2b = a + c, replace c with a-6<BR>\n" );
document.write( "2b = a + a - 6<BR>\n" );
document.write( "2b = 2a - 6<BR>\n" );
document.write( "Simplify, divide by 2<BR>\n" );
document.write( "b = a - 3<BR>\n" );
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document.write( "Back to the 2nd eq: 100a + c = 158b + 12, replace b with (a-3), c with (a-6)<BR>\n" );
document.write( "100a + (a-6) = 158(a-3) + 12<BR>\n" );
document.write( "101a = 158a - 474 + 12 + 6<BR>\n" );
document.write( "101a - 158a = -474 + 18<BR>\n" );
document.write( "57a = 456<BR>\n" );
document.write( "a = 456/57<BR>\n" );
document.write( "a = 8 is the first digit<BR>\n" );
document.write( "then<BR>\n" );
document.write( "b = 8 - 3<BR>\n" );
document.write( "b = 5<BR>\n" );
document.write( "and<BR>\n" );
document.write( "c = 8 - 6<BR>\n" );
document.write( "c = 2<BR>\n" );
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document.write( "Find the no. 852<BR>\n" );
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document.write( "You can check this for yourself in each statement.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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