document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=744940>Question 744940</A>: <I><SPAN STYLE=\"word-break: break-all;\"> three solutions contain a certain acid. the first contains 15% acid, the second 35%, and the third 40%. A chemist wishes to use all three solutions to obtain a 75-liter mixture containing 34% acid. If the chemist wants to use twice as much of the 35% solution as of the 40% solution, how many liters, to the nearest 10th, of each solution should be used? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #453617 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=453617\">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 40% solution needed<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2a+ ALIGN=MIDDLE  ALT=\"+2a+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = liters of 35% 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 15% solution needed<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.4a+ ALIGN=MIDDLE  ALT=\"+.4a+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = liters of acid in 40% solution<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.35%2A2a+=+.7a+ ALIGN=MIDDLE  ALT=\"+.35%2A2a+=+.7a+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = liters of acid in 35% solution<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.15b+ ALIGN=MIDDLE  ALT=\"+.15b+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = liters of acid in 15% solution<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+%2B+2a+%2B+b+=+75+ ALIGN=MIDDLE  ALT=\"+a+%2B+2a+%2B+b+=+75+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+.4a+%2B+.7a+%2B+.15b+%29+%2F+75+=+.34+ ALIGN=MIDDLE  ALT=\"+%28+.4a+%2B+.7a+%2B+.15b+%29+%2F+75+=+.34+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3a+%2B+b+=+75+ ALIGN=MIDDLE  ALT=\"+3a+%2B+b+=+75+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1.1a+%2B+.15b+=+.34%2A75+ ALIGN=MIDDLE  ALT=\"+1.1a+%2B+.15b+=+.34%2A75+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1.1a+%2B+.15b+=+25.5+ ALIGN=MIDDLE  ALT=\"+1.1a+%2B+.15b+=+25.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+110a+%2B+15b+=+2550+ ALIGN=MIDDLE  ALT=\"+110a+%2B+15b+=+2550+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "Multiply both sides of (1) by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+15+ ALIGN=MIDDLE  ALT=\"+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and subtract (1) from (2)<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+110a+%2B+15b+=+2550+ ALIGN=MIDDLE  ALT=\"+110a+%2B+15b+=+2550+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-45a+-+15b+=+-1125+ ALIGN=MIDDLE  ALT=\"+-45a+-+15b+=+-1125+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+65a+=+1425+ ALIGN=MIDDLE  ALT=\"+65a+=+1425+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+21.9+ ALIGN=MIDDLE  ALT=\"+a+=+21.9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2a+=+43.8+ ALIGN=MIDDLE  ALT=\"+2a+=+43.8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and, since<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3a+%2B+b+=+75+ ALIGN=MIDDLE  ALT=\"+3a+%2B+b+=+75+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%2A21.9+%2B+b+=+75+ ALIGN=MIDDLE  ALT=\"+3%2A21.9+%2B+b+=+75+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+65.8+%2B+b+=+75+ ALIGN=MIDDLE  ALT=\"+65.8+%2B+b+=+75+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+9.2+ ALIGN=MIDDLE  ALT=\"+b+=+9.2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "21.9 liters of 40% solution are needed<BR>\n" );
document.write( "43.8 liters of 35% solution needed<BR>\n" );
document.write( "9.2 liters of 15% solution are needed<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+.4a+%2B+.7a+%2B+.15b+%29+%2F+75+=+.34+ ALIGN=MIDDLE  ALT=\"+%28+.4a+%2B+.7a+%2B+.15b+%29+%2F+75+=+.34+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+1.1%2A21.9+%2B+.15%2A9.2+%29+%2F+75+=+.34+ ALIGN=MIDDLE  ALT=\"+%28+1.1%2A21.9+%2B+.15%2A9.2+%29+%2F+75+=+.34+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++24.1+%2B+1.4+=+.34%2A75+ ALIGN=MIDDLE  ALT=\"++24.1+%2B+1.4+=+.34%2A75+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+25.5+=+25.5+ ALIGN=MIDDLE  ALT=\"+25.5+=+25.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );