document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1102100>Question 1102100</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A 20% solution of fertilizer is to be mixed with a 50% solution of fertilizer in order to get 60 gallons of a 40% solution. How many gallons of the 20% and 50% solution should be mixed? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #716739 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=716739\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let A denote the 50% solution and B denote the 20% solution which we have.<BR>\n" );
document.write( "Let C denote the 40% solution which we want.<BR>\n" );
document.write( "Using the method of alligation.<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "50         20 20/30*60=40 gal of 50% solution\r\n" );
document.write( "      40     40+20= 60 gal of 40% solution\r\n" );
document.write( "20         10 10/30*60=20 gal of 20% solution\r\n" );
document.write( "           30\r\n" );
document.write( "</PRE><BR>\n" );
document.write( "10= 50 - 40<BR>\n" );
document.write( "20= 40 - 20<BR>\n" );
document.write( "20+10=30 parts total<BR>\n" );
document.write( "There are 60 gal total<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "50         20 20/30*60=40 gal of 50% solution\r\n" );
document.write( "</PRE><BR>\n" );
document.write( "20/30*60=40<BR>\n" );
document.write( "40 gal of 50% solution.<BR>\n" );
document.write( "60-40=20 gal<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "20         10 10/30*60=20 gal of 20% solution\r\n" );
document.write( "</PRE><BR>\n" );
document.write( "20 gal of 20% solution.\r<BR>\n" );
document.write( "\n" );
document.write( "check<BR>\n" );
document.write( "0.2 * 20 + 0.5 * 40 = 0.4*60<BR>\n" );
document.write( "4.0 + 20.0 = 24.0<BR>\n" );
document.write( "24.0 = 24.0<BR>\n" );
document.write( "ok\r<BR>\n" );
document.write( "\n" );
document.write( "Now using algebra<BR>\n" );
document.write( "We need a total of 60 gal at 40%<BR>\n" );
document.write( "We want to know how many gal at 20% to mix with 50%<BR>\n" );
document.write( "a+b=60<BR>\n" );
document.write( "0.2*a+0.5*b=0.4*60<BR>\n" );
document.write( "a=60-b<BR>\n" );
document.write( "0.2*(60-b)+0.5*b=24<BR>\n" );
document.write( "12-0.2b+0.5*b=24<BR>\n" );
document.write( "0.3*b=12<BR>\n" );
document.write( "b=40<BR>\n" );
document.write( "a=60-b<BR>\n" );
document.write( "a=20 gal at 20%<BR>\n" );
document.write( "b=40 gal at 50%<BR>\n" );
document.write( "check<BR>\n" );
document.write( "0.2*20+0.5*40=0.4*60<BR>\n" );
document.write( "4+20=24<BR>\n" );
document.write( "24=24<BR>\n" );
document.write( "ok<BR>\n" );
document.write( "codemx1<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );