document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=573587>Question 573587</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the sum of two positive integers is 30 and their product is 216, find the positive difference between the two numbers </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #368873 by </B><A HREF=/tutors/aboutme.mpl?userid=mathsmiles><B>mathsmiles(68)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathsmiles><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=mathsmiles><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=368873\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's let X and Y be the two numbers we need to search for.<BR>\n" );
document.write( "Their sum is 30 so <BR>\n" );
document.write( "X + Y = 30<BR>\n" );
document.write( "their product is 216 so<BR>\n" );
document.write( "XY = 216\r<BR>\n" );
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document.write( "Let's use substitution method, so need to get X or Y by itself in one of these equations.  I'll pick the 1st equation since you asked for my help and I get some perk for doing this.  :-)\r<BR>\n" );
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document.write( "X + Y = 30<BR>\n" );
document.write( "Subtracting Y from both sides:<BR>\n" );
document.write( "X = 30 - Y\r<BR>\n" );
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document.write( "Now substitute this into the 2nd equation for X:<BR>\n" );
document.write( "XY = 216<BR>\n" );
document.write( "(30-Y)(Y) = 216<BR>\n" );
document.write( "Multiplying out:<BR>\n" );
document.write( "30Y - Y^2 = 216   Let's move everything to the right<BR>\n" );
document.write( "-30Y + Y^2   -30Y + Y^2<BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "0 = Y^2 - 30Y + 216\r<BR>\n" );
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document.write( "(Y - )(Y - )  Need to find two factors of 216 which add up to 30.  (Ugh! This is the worst part!!)<BR>\n" );
document.write( "The factors of 216 are:<BR>\n" );
document.write( "1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216<BR>\n" );
document.write( "Lucky for me, I found <BR>\n" );
document.write( "http://www.calculatorsoup.com/calculators/math/factors.php\r<BR>\n" );
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document.write( "See two factors which add to 30 and also multiply to get 216?<BR>\n" );
document.write( "18 and 12\r<BR>\n" );
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document.write( "(Y - 18)(Y - 12) = 0<BR>\n" );
document.write( "Let's check and make sure we get the original equation using FOIL:<BR>\n" );
document.write( "Y^2 - 12Y - 18Y + 216 = Y^2 - 30Y + 216   Ok, good.\r<BR>\n" );
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document.write( "Solving for Y:<BR>\n" );
document.write( "Y - 18 = 0 <BR>\n" );
document.write( "Y = 18 <BR>\n" );
document.write( "AND <BR>\n" );
document.write( "Y - 12 = 0<BR>\n" );
document.write( "Y = 12<BR>\n" );
document.write( "Looks like we have our two numbers.  Now go back to the original question:\r<BR>\n" );
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document.write( "Find the positive difference between the two numbers:<BR>\n" );
document.write( "18 and 12<BR>\n" );
document.write( "18 - 12 = 6  That's the answer!<BR>\n" );
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