document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=462311>Question 462311</A>: <I><SPAN STYLE=\"word-break: break-all;\"> two numbers total 78 and have a difference of 6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #316939 by </B><A HREF=/tutors/aboutme.mpl?userid=math-vortex><B>math-vortex(648)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math-vortex><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=math-vortex><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=316939\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Two numbers total 78 and have a difference of 6. I presume that you want to know what the two numbers are. <BR>\n" );
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document.write( "Let<BR>\n" );
document.write( "x = the first number<BR>\n" );
document.write( "y = the second number<BR>\n" );
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document.write( "The sum of the two numbers is 78. Using algebra, we write the equation,<BR>\n" );
document.write( "x + y = 78<BR>\n" );
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document.write( "The difference between the number is 6. Using algebra, we write,<BR>\n" );
document.write( "x - y = 6<BR>\n" );
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document.write( "Now we have a system of two equations in two variables. The system lends itself nicely to solving by elimination. Add the two equations together.<BR>\n" );
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document.write( "x + y = 78<BR>\n" );
document.write( "x - y =  6<BR>\n" );
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document.write( "2x + 0 = 84<BR>\n" );
document.write( "x = 42<BR>\n" );
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document.write( "Now we know that the first number is 42. Since the difference between the two numbers is 6, the second number is 42 - 6 = 36.<BR>\n" );
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document.write( "The sum of 42 and 36 is 78, so these are our two numbers.<BR>\n" );
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document.write( "I solved this using a system of linear equations. You can also solve it by writing an expression for the 2nd number in terms of x. <BR>\n" );
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document.write( "Let <BR>\n" );
document.write( "x = 1st number<BR>\n" );
document.write( "x - 6 = 2nd number<BR>\n" );
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document.write( "The sum of the two numbers is 78, so<BR>\n" );
document.write( "x + (x-6) = 78<BR>\n" );
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document.write( "Now solve for x, and proceed as I did above.<BR>\n" );
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document.write( "hope this helps!<BR>\n" );
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document.write( "Ms.Figgy<BR>\n" );
document.write( "math.in.the.vortex<BR>\n" );
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