document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=360239>Question 360239</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For a certain 3-digit number, interchanging the first and last digits gives a 3-digit number 297 less than the original number. Doubling the first and last digits of the original number gives a 3-digit number and increases the sum of the digits to 15 what is 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 #257062 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=257062\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let 100x + 10y + z = a three digit number<BR>\n" );
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document.write( "Write an equation for each statement:<BR>\n" );
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document.write( "For a certain 3-digit number, interchanging the first and last digits gives<BR>\n" );
document.write( " a 3-digit number 297 less than the original number.<BR>\n" );
document.write( "100x + 10y + z = 100z + 10y + x + 297<BR>\n" );
document.write( "100x - x + 10y - 10y = 100z - z + 297<BR>\n" );
document.write( "99x = 99z + 297<BR>\n" );
document.write( "Simplify, divide thru by 99<BR>\n" );
document.write( "x = z + 3<BR>\n" );
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document.write( "Doubling the first and last digits of the original number gives a 3-digit<BR>\n" );
document.write( " number and increases the sum of the digits to 15<BR>\n" );
document.write( "2x + y + 2z = 15<BR>\n" );
document.write( "Replace x with (z+3)<BR>\n" );
document.write( "2(z+3) + y + 2z = 15<BR>\n" );
document.write( "2z + 6 + y + 2z = 15<BR>\n" );
document.write( "4z + y = 15 - 6<BR>\n" );
document.write( "4z + y = 9<BR>\n" );
document.write( "y = -4z + 9<BR>\n" );
document.write( "only two positive integer solutions here<BR>\n" );
document.write( "z=1, y=5, then x=4<BR>\n" );
document.write( "451 is the number<BR>\n" );
document.write( "and<BR>\n" );
document.write( "z=2, y=1, then x=5<BR>\n" );
document.write( "512 is the number, however, it says:<BR>\n" );
document.write( "\"Doubling the first and last digits gives a 3-digit number\", so it can,t be 512<BR>\n" );
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document.write( " what is the number? 451 <BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "451 - 154 = 297<BR>\n" );
document.write( " </SPAN>\n" );
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