document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=164602>Question 164602</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a three digit number whose tens digit is 4 times the hundred’s digit and the unit’s digit is one more than the ten’s digit. The square of the sum of the digits is 72 more than 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 #121300 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=121300\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's call the hundreds' digit A, tens' digit B, and ones' digit C.<BR>\n" );
document.write( "The number is ABC, or numerically A*100+B*10+C.<BR>\n" );
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document.write( "\"tens digit is 4 times the hundred’s digit\" <BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=4A ALIGN=MIDDLE  ALT=\"B=4A\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "\"unit’s digit is one more than the ten’s digit\"<BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=1%2BB=1%2B4A ALIGN=MIDDLE  ALT=\"C=1%2BB=1%2B4A\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "\"square of the sum of the digits is 72 more than the number\"<BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E2%2BB%5E2%2BC%5E2=A%2A100%2BB%2A10%2BC%2B72 ALIGN=MIDDLE  ALT=\"A%5E2%2BB%5E2%2BC%5E2=A%2A100%2BB%2A10%2BC%2B72\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Use eqs.1 and 2 and substitute for B and C in eq. 3 and solve for A.<BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E2%2BB%5E2%2BC%5E2=A%2A100%2BB%2A10%2BC%2B72 ALIGN=MIDDLE  ALT=\"A%5E2%2BB%5E2%2BC%5E2=A%2A100%2BB%2A10%2BC%2B72\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E2%2B%284A%29%5E2%2B%281%2B4A%29%5E2=A%2A100%2B%284A%29%2A10%2B%281%2B4A%29%2B72 ALIGN=MIDDLE  ALT=\"A%5E2%2B%284A%29%5E2%2B%281%2B4A%29%5E2=A%2A100%2B%284A%29%2A10%2B%281%2B4A%29%2B72\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E2%2B16A%5E2%2B1%2B8A%2B16A%5E2=100A%2B40A%2B1%2B4A%2B72 ALIGN=MIDDLE  ALT=\"A%5E2%2B16A%5E2%2B1%2B8A%2B16A%5E2=100A%2B40A%2B1%2B4A%2B72\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=33A%5E2%2B8A%2B1=144A%2B73 ALIGN=MIDDLE  ALT=\"33A%5E2%2B8A%2B1=144A%2B73\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=33A%5E2-136A-72=0 ALIGN=MIDDLE  ALT=\"33A%5E2-136A-72=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This quadratic equation does not have an integer solution. <BR>\n" );
document.write( "Please check the problem set-up because something is wrong.<BR>\n" );
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document.write( "The only possible number choices are 001, 145, and 289. <BR>\n" );
document.write( "The \"sum of the squares\" for those are : 1, 42, 149.<BR>\n" );
document.write( "While  \"72 more than the number\" is: 73, 217, 361.<BR>\n" );
document.write( "Clearly the last two lines aren't equal.<BR>\n" );
document.write( "There is no solution the way the problem is set up. <BR>\n" );
document.write( "Please check and re-post.  </SPAN>\n" );
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