document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=269223>Question 269223</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Gerry mixes different solutions with concentrations of 25%, 40%, and 50% to get 200 liters fo a 32% solution.  Also, it takes twice the liters of the 40% solution to equal the same liters of the 25% , find how mnay liters of each kind he uses.\r<BR>\n" );
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document.write( "I have set up a table, but do not understand how the 50% factors in.  Please help.  Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #197358 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=197358\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > = liters of 25% solution needed<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > = liters of 40% solution needed<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > = liters of 50% solution needed<BR>\n" );
document.write( "given:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+b+%2B+c+=+200 ALIGN=MIDDLE  ALT=\"a+%2B+b+%2B+c+=+200\"   DISABLED_style= \"max-width:90%; height:auto;\" > liters<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+2b ALIGN=MIDDLE  ALT=\"a+=+2b\"   DISABLED_style= \"max-width:90%; height:auto;\" > liters<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28.25a+%2B+.4b+%2B+.5c%29%2F200+=+.32 ALIGN=MIDDLE  ALT=\"%28.25a+%2B+.4b+%2B+.5c%29%2F200+=+.32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28.25a+%2B+.4b+%2B+.5c%29%2F200+=+64 ALIGN=MIDDLE  ALT=\"%28.25a+%2B+.4b+%2B+.5c%29%2F200+=+64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25a+%2B+40b+%2B+50c+=+6400 ALIGN=MIDDLE  ALT=\"25a+%2B+40b+%2B+50c+=+6400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides of (1) by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25 ALIGN=MIDDLE  ALT=\"25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and subtract from (3)<BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25a+%2B+40b+%2B+50c+=+6400 ALIGN=MIDDLE  ALT=\"25a+%2B+40b+%2B+50c+=+6400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-25a+-+25b+-+25c+=+5000 ALIGN=MIDDLE  ALT=\"-25a+-+25b+-+25c+=+5000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15b+%2B+25c+=+1400 ALIGN=MIDDLE  ALT=\"15b+%2B+25c+=+1400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3b+%2B+5c+=+280 ALIGN=MIDDLE  ALT=\"3b+%2B+5c+=+280\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5c+=+280+-+3b ALIGN=MIDDLE  ALT=\"5c+=+280+-+3b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+56+-+%283%2F5%29%2Ab ALIGN=MIDDLE  ALT=\"c+=+56+-+%283%2F5%29%2Ab\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Going back to (1)<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+b+%2B+c+=+200 ALIGN=MIDDLE  ALT=\"a+%2B+b+%2B+c+=+200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b+%2B+b+%2B+56+-+%283%2F5%29%2Ab+=+200 ALIGN=MIDDLE  ALT=\"2b+%2B+b+%2B+56+-+%283%2F5%29%2Ab+=+200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3b+-+%283%2F5%29%2Ab+=+144 ALIGN=MIDDLE  ALT=\"3b+-+%283%2F5%29%2Ab+=+144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15b+-+3b+=+720 ALIGN=MIDDLE  ALT=\"15b+-+3b+=+720\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12b+=+720 ALIGN=MIDDLE  ALT=\"12b+=+720\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+60 ALIGN=MIDDLE  ALT=\"b+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And, since<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+2b ALIGN=MIDDLE  ALT=\"a+=+2b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+2%2A60 ALIGN=MIDDLE  ALT=\"a+=+2%2A60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+120 ALIGN=MIDDLE  ALT=\"a+=+120\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+b+%2B+c+=+200 ALIGN=MIDDLE  ALT=\"a+%2B+b+%2B+c+=+200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120+%2B+60+%2B+c+=+200 ALIGN=MIDDLE  ALT=\"120+%2B+60+%2B+c+=+200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+20 ALIGN=MIDDLE  ALT=\"c+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "120 liters of 25% solution are needed<BR>\n" );
document.write( "60 liters of 40% solution are needed<BR>\n" );
document.write( "20 liters of 50% solution are needed<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28.25a+%2B+.4b+%2B+.5c%29%2F200+=+.32 ALIGN=MIDDLE  ALT=\"%28.25a+%2B+.4b+%2B+.5c%29%2F200+=+.32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28.25%2A120+%2B+.4%2A60+%2B+.5%2A20%29%2F200+=+.32 ALIGN=MIDDLE  ALT=\"%28.25%2A120+%2B+.4%2A60+%2B+.5%2A20%29%2F200+=+.32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2830+%2B+24+%2B+10%29%2F200+=+.32 ALIGN=MIDDLE  ALT=\"%2830+%2B+24+%2B+10%29%2F200+=+.32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64%2F200+=+.32 ALIGN=MIDDLE  ALT=\"64%2F200+=+.32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64+=+64+ ALIGN=MIDDLE  ALT=\"64+=+64+\"   DISABLED_style= \"max-width:90%; height:auto;\" > OK\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );