document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=829757>Question 829757</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A number is between 20 and 30 and is three times the sum of its digits.  What is the number?<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 #500085 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=500085\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Two-digit number, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2A10%2By%2A1 ALIGN=MIDDLE  ALT=\"x%2A10%2By%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Expect the number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x%2By%3E20 ALIGN=MIDDLE  ALT=\"10x%2By%3E20\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x%2By%3C30 ALIGN=MIDDLE  ALT=\"10x%2By%3C30\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "We must expect only Natural Numbers for x and y, so if graphing, these must be only in quadrant 1.\r<BR>\n" );
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document.write( "The other part of the description:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%283%28x%2By%29=10x%2By%29 ALIGN=MIDDLE  ALT=\"highlight_green%283%28x%2By%29=10x%2By%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Simplify.<BR>\n" );
document.write( "3x+3y=10x+y<BR>\n" );
document.write( "3y=7x+y<BR>\n" );
document.write( "2y=7x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28-7x%2B2y=0%29 ALIGN=MIDDLE  ALT=\"highlight_green%28-7x%2B2y=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Next plan is that we can plot that line.  Intercepts are (0,0) only.  The equation can be shown as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%287%2F2%29x ALIGN=MIDDLE  ALT=\"y=%287%2F2%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >; and because of the inequalities expected above, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E-10x%2B20 ALIGN=MIDDLE  ALT=\"y%3E-10x%2B20\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C-10x%2B30 ALIGN=MIDDLE  ALT=\"y%3C-10x%2B30\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The easiest path seems to be find all the Natural Number coordinate pairs on the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%287%2F2%29x ALIGN=MIDDLE  ALT=\"y=%287%2F2%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and stay at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C10 ALIGN=MIDDLE  ALT=\"y%3C10\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Best guess it the point, (2,7).<BR>\n" );
document.write( "The number, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28highlight%2827%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28highlight%2827%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ?<BR>\n" );
document.write( "No other  natural number combination on that line for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C10 ALIGN=MIDDLE  ALT=\"y%3C10\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "CHECK THIS:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%282%2B7%29=27 ALIGN=MIDDLE  ALT=\"3%282%2B7%29=27\"   DISABLED_style= \"max-width:90%; height:auto;\" >?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%289%29=27 ALIGN=MIDDLE  ALT=\"3%289%29=27\"   DISABLED_style= \"max-width:90%; height:auto;\" > yes. </SPAN>\n" );
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