document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=108952>Question 108952</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/015320785x/algebrahomeworkh>Harcourt Math Practice Workbook</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Two numbers have a difference of 10 and the sum of 34.  What are the numbers?\r<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 #79445 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=79445\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Call the two unknown numbers x and y.<BR>\n" );
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document.write( "Since their difference is 10 you can write the equation:<BR>\n" );
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document.write( "x - y = 10<BR>\n" );
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document.write( "And since their sum is 34 you can write the equation:<BR>\n" );
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document.write( "x + y = 34<BR>\n" );
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document.write( "Write the two equations one above the other:<BR>\n" );
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document.write( "x - y = 10<BR>\n" );
document.write( "x + y = 34<BR>\n" );
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document.write( "Note that if you add the two equations vertically in columns that the -y of the top equation<BR>\n" );
document.write( "will cancel the +y of the bottom equation. So, adding vertically results in the x + x = 2x,<BR>\n" );
document.write( "the two y terms cancel, and on the right side the 10 + 34 = 44<BR>\n" );
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document.write( "Therefore, the result of the addition is:<BR>\n" );
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document.write( "2x = 44<BR>\n" );
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document.write( "And if you divide both sides of this equation by 2 you get:<BR>\n" );
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document.write( "x = 22<BR>\n" );
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document.write( "Since x + y is to equal 34, then you can write:<BR>\n" );
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document.write( "22 + y = 34<BR>\n" );
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document.write( "Subtracting 22 from both sides of this equation results in:<BR>\n" );
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document.write( "y = 12<BR>\n" );
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document.write( "So the answer to this problem is that one of the numbers is 22 and the other is 12. <BR>\n" );
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document.write( "As a check, note that the difference of the two numbers is 22 - 12 = 10 and the sum of the<BR>\n" );
document.write( "two numbers is 22 + 12 = 34, just as the problem says things should be.<BR>\n" );
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document.write( "Hope this helps you to understand the problem a little better.<BR>\n" );
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