document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=633693>Question 633693</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a certain three digit number, the hundreds digit is the sum of the other two digits. If the units and tens digits of this number are interchanged,the new number is 9 more than the original number.  If the hundreds and ten digits of the original number are interchanged, the new number is 360 less than the original number. Find the original number.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #399151 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=399151\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The three digits: a, b, c; write an equation for each statement<BR>\n" );
document.write( "Simplify each equation as much as possible<BR>\n" );
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document.write( "In a certain three digit number,<BR>\n" );
document.write( "100a + 10b + c<BR>\n" );
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document.write( " the hundreds digit is the sum of the other two digits.<BR>\n" );
document.write( "a = b + c<BR>\n" );
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document.write( "If the units and tens digits of this number are interchanged,the new number<BR>\n" );
document.write( " is 9 more than the original number.<BR>\n" );
document.write( "100a + 10c + b = 100a + 10b + c + 9<BR>\n" );
document.write( "Subtract 100a from both sides<BR>\n" );
document.write( "10c + b = 10b + c + 9<BR>\n" );
document.write( "10c - c = 10b - b + 9<BR>\n" );
document.write( "9c = 9b + 9<BR>\n" );
document.write( "simplify, divide by 9<BR>\n" );
document.write( "c = b + 1<BR>\n" );
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document.write( "If the hundreds and ten digits of the original number are interchanged,<BR>\n" );
document.write( " the new number is 360 less than the original number.<BR>\n" );
document.write( "100b + 10a + c = 100a + 10b + c - 360<BR>\n" );
document.write( "subtract c from both sides<BR>\n" );
document.write( "100b + 10a = 100a + 10b - 360<BR>\n" );
document.write( "100b - 10b = 100a - 10a - 360<BR>\n" );
document.write( "90b = 90a - 360<BR>\n" );
document.write( "Simplify, divide by 90<BR>\n" );
document.write( "b = a - 4<BR>\n" );
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document.write( "a = b + 4<BR>\n" );
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document.write( "Using the equation: a = b + c, replace a and c<BR>\n" );
document.write( "(b+4) = b + (b+1)<BR>\n" );
document.write( "4 - 1 = 2b - b<BR>\n" );
document.write( "3 = b<BR>\n" );
document.write( "then<BR>\n" );
document.write( "a = 3 + 4<BR>\n" );
document.write( "a = 7<BR>\n" );
document.write( "and<BR>\n" );
document.write( "c = 3 + 1<BR>\n" );
document.write( "c = 4<BR>\n" );
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document.write( "734 is the original number<BR>\n" );
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document.write( "You can confirm this solution in the last two statements\r<BR>\n" );
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