document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=71829>Question 71829</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The difference of two numbers is 11. The second is 8 less than 2 times the first. What are 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 #51395 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=51395\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let A represent the first number and B represent the second number.  <BR>\n" );
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document.write( "In the problem the first sentence says that difference in these two numbers is 11. Therefore,<BR>\n" );
document.write( "you can write the equation for this difference as:<BR>\n" );
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document.write( "A - B = 11<BR>\n" );
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document.write( "The second sentence says the second number (B) is 8 less than 2 times the first. <BR>\n" );
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document.write( "Two times the first is 2A and 8 less than that is, therefore, 2A - 8.  Since this is to<BR>\n" );
document.write( "equal the second (B) we can write the equation:<BR>\n" );
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document.write( "2A - 8 = B<BR>\n" );
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document.write( "Notice that from this second equation we have a value for B in terms of A.  Let's take<BR>\n" );
document.write( "the left side of this equation (that is take 2A - 8) and plug it into our first equation<BR>\n" );
document.write( "in place of B. When we do the first equation becomes:<BR>\n" );
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document.write( "A - (2A - 8) = 11<BR>\n" );
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document.write( "Clear the parens by changing the terms inside to get:<BR>\n" );
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document.write( "A - 2A + 8 = 11<BR>\n" );
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document.write( "Combine the A terms to get:<BR>\n" );
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document.write( "-A + 8 = 11<BR>\n" );
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document.write( "Subtract 8 from both sides to get rid of it on the left side:<BR>\n" );
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document.write( "-A = 3<BR>\n" );
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document.write( "Multiply both sides by -1 and the answer for A is:<BR>\n" );
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document.write( "A = -3<BR>\n" );
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document.write( "Then you can take this value and substitute is for A in either of our two original <BR>\n" );
document.write( "equations.<BR>\n" );
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document.write( "Let's substitute it into the first equation of A - B = 11.  When you do you get:<BR>\n" );
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document.write( "-3 - B = 11<BR>\n" );
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document.write( "Add + 3 to both sides to get rid of the -3 on the left side:<BR>\n" );
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document.write( "  -B = 14<BR>\n" );
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document.write( "And multiply both sides by -1 to solve for B.  The result is:<BR>\n" );
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document.write( "B = -14<BR>\n" );
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document.write( "As a further check is -14 actually 8 less than 2 times (-3).  It is and the answer <BR>\n" );
document.write( "checks.<BR>\n" );
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document.write( "Hope this helps you to see how to work the problem.  The big trick to problems such as<BR>\n" );
document.write( "these is to analyze the words and translate them into correct equations.  The rest is<BR>\n" );
document.write( "straightforward math.<BR>\n" );
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