document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=137580>Question 137580</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780495078814/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The sum of two numbers is twice their difference. The larger number is 6 more than twice the smaller. Find the numbers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #100643 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=100643\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=the larger number<BR>\n" );
document.write( "and y=the smaller number\r<BR>\n" );
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document.write( "Now we are told that:\r<BR>\n" );
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document.write( "x+y=2(x-y) or<BR>\n" );
document.write( "x+y=2x-2y subtract x and also y from each side<BR>\n" );
document.write( "0=2x-x-2y-y  collect like terms<BR>\n" );
document.write( " x-3y=0---------------------------------------------eq1\r<BR>\n" );
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document.write( "We are also told that:<BR>\n" );
document.write( "x=2y+6  subtract 2y from each side\r<BR>\n" );
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document.write( "x-2y=2y-2y+6<BR>\n" );
document.write( "x-2y=6---------------------------------------------eq2<BR>\n" );
document.write( "From eq1, we see that x=3y.  Substitute this into eq2<BR>\n" );
document.write( "3y-2y=6<BR>\n" );
document.write( "y=6---------------------------------------smaller number<BR>\n" );
document.write( "substitute y=6 into eq1\r<BR>\n" );
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document.write( "x-18=0  add 18 to each side\r<BR>\n" );
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document.write( "x=18-------------------------------------larger number\r<BR>\n" );
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document.write( "CK<BR>\n" );
document.write( "The sum of two numbers is twice their difference:<BR>\n" );
document.write( "6+18=2*(18-6)<BR>\n" );
document.write( "24=2*12<BR>\n" );
document.write( "24=24<BR>\n" );
document.write( "The larger number is 6 more than twice the smaller.<BR>\n" );
document.write( "18=2*6+6<BR>\n" );
document.write( "18=12+6<BR>\n" );
document.write( "18=18\r<BR>\n" );
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document.write( "Hope this helps---ptaylor </SPAN>\n" );
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