document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1112145>Question 1112145</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Separate 800 into three parts, such that the sum of the first, 1/2 of the second, and 2/5 of the third is 400; and the sum of the second, 3/4 of the first, and 1/4 of the third is 400. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #727206 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=727206\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The given information tells us...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%2Bz+=+800 ALIGN=MIDDLE  ALT=\"x%2By%2Bz+=+800\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (1)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B%281%2F2%29y%2B%282%2F5%29z+=+400 ALIGN=MIDDLE  ALT=\"x%2B%281%2F2%29y%2B%282%2F5%29z+=+400\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F4%29x%2By%2B%281%2F4%29z+=+400 ALIGN=MIDDLE  ALT=\"%283%2F4%29x%2By%2B%281%2F4%29z+=+400\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (3)<br><BR>\n" );
document.write( "Solve the system by first eliminating one variable to reduce the problem to two equations in two variables.  With the given coefficients, eliminating y first looks to be the easiest.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%2Bz+=+800 ALIGN=MIDDLE  ALT=\"x%2By%2Bz+=+800\"   DISABLED_style= \"max-width:90%; height:auto;\" >; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2By%2B%284%2F5%29z+=+800 ALIGN=MIDDLE  ALT=\"2x%2By%2B%284%2F5%29z+=+800\"   DISABLED_style= \"max-width:90%; height:auto;\" >; --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2B%281%2F5%29z+=+0 ALIGN=MIDDLE  ALT=\"-x%2B%281%2F5%29z+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%2Bz+=+800 ALIGN=MIDDLE  ALT=\"x%2By%2Bz+=+800\"   DISABLED_style= \"max-width:90%; height:auto;\" >; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F4%29x%2By%2B%281%2F4%29z+=+400 ALIGN=MIDDLE  ALT=\"%283%2F4%29x%2By%2B%281%2F4%29z+=+400\"   DISABLED_style= \"max-width:90%; height:auto;\" >; --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29x%2B%283%2F4%29z+=+400 ALIGN=MIDDLE  ALT=\"%281%2F4%29x%2B%283%2F4%29z+=+400\"   DISABLED_style= \"max-width:90%; height:auto;\" >  -->  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3z+=+1200 ALIGN=MIDDLE  ALT=\"x%2B3z+=+1200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Adding the last two equations,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816%2F5%29z+=+1600 ALIGN=MIDDLE  ALT=\"%2816%2F5%29z+=+1600\"   DISABLED_style= \"max-width:90%; height:auto;\" >  -->  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+500 ALIGN=MIDDLE  ALT=\"z+=+500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Plugging back into earlier equations, x=100 and y=200.<br><BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%2B200%2B500+=+800 ALIGN=MIDDLE  ALT=\"100%2B200%2B500+=+800\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%2B%281%2F2%29200%2B%282%2F5%29500+=+100%2B100%2B200+=+400 ALIGN=MIDDLE  ALT=\"100%2B%281%2F2%29200%2B%282%2F5%29500+=+100%2B100%2B200+=+400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "{{(3/4)(100)+200+(1/4)(500) = 75+200+125 = 400}}}<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );