document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1061097>Question 1061097</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if a chemist needs a 40% acid solution, how much 50% solution needs to be mixed with 8 liters of a 25% solution to obtain the desired concentration? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #675916 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=675916\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >= volume of 50% solution needed (in Liters)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" >= volume of 25% solution used (in Liters)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V ALIGN=MIDDLE  ALT=\"V\"   DISABLED_style= \"max-width:90%; height:auto;\" >= volume of the final 40% solution mixture (in Liters)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.5x ALIGN=MIDDLE  ALT=\"0.5x\"   DISABLED_style= \"max-width:90%; height:auto;\" >= amount of acid in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Liters of 50% solution<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.25%2A8 ALIGN=MIDDLE  ALT=\"0.25%2A8\"   DISABLED_style= \"max-width:90%; height:auto;\" >= amount of acid in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Liters of 25% solution<BR>\n" );
document.write( "We need to make it so that<BR>\n" );
document.write( "{{A=0.40V}}}= amount of acid in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V ALIGN=MIDDLE  ALT=\"V\"   DISABLED_style= \"max-width:90%; height:auto;\" > Liters of 40% solution<BR>\n" );
document.write( "We know that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=0.5x%2B0.25%2A8 ALIGN=MIDDLE  ALT=\"A=0.5x%2B0.25%2A8\"   DISABLED_style= \"max-width:90%; height:auto;\" >= amount of acid in the final mixture<BR>\n" );
document.write( "We assume that there was no substantial volume change on mixing, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=8%2Bx ALIGN=MIDDLE  ALT=\"V=8%2Bx\"   DISABLED_style= \"max-width:90%; height:auto;\" >= final volume (assumed, in Liters)<BR>\n" );
document.write( "We can solve (the system of the last 3 equations) for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V ALIGN=MIDDLE  ALT=\"V\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "or we can combine the 3 equations into one as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.40%288%2Bx%29=0.5x%2B0.25%2A8 ALIGN=MIDDLE  ALT=\"0.40%288%2Bx%29=0.5x%2B0.25%2A8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Solving:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.4%288%2Bx%29=0.5x%2B0.25%2A8 ALIGN=MIDDLE  ALT=\"0.4%288%2Bx%29=0.5x%2B0.25%2A8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.2%2B0.4x=0.5x%2B2.0 ALIGN=MIDDLE  ALT=\"3.2%2B0.4x=0.5x%2B2.0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.2-2.0=0.5x-0.4x ALIGN=MIDDLE  ALT=\"3.2-2.0=0.5x-0.4x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.2=0.1x ALIGN=MIDDLE  ALT=\"1.2=0.1x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1.2%2F0.1 ALIGN=MIDDLE  ALT=\"x=1.2%2F0.1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=12 ALIGN=MIDDLE  ALT=\"x=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "We need to mix <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2812%29 ALIGN=MIDDLE  ALT=\"highlight%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Liters of 50% solution with the 8 Liters of 25% solution to obtain the desired concentration.<BR>\n" );
document.write( "Bonus answer:<BR>\n" );
document.write( "We expect to end up with a final volume (in liters) of<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=8%2B12=20 ALIGN=MIDDLE  ALT=\"V=8%2B12=20\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "NOTEs:<BR>\n" );
document.write( "When you mix to solutions the final volume is not exactly the sum of the volumes mixed, but in many cases it will be close enough for your purposes <BR>\n" );
document.write( " <BR>\n" );
document.write( "\"Acid\" does not identify any chemical, or mixture of compounds.<BR>\n" );
document.write( "In chemistry, it identify a very broad class of chemical compounds. Exanples: ascorbic acid (also known as vitamin C), acetylsalicylic (also known as aspirin), acetic acid (the chemical compound present, along with a lot of water, in vinegar), hydrochloric acid (a solution of the gas hydrogen chloride in water, at a concentration of about 36 grams gas per 100 grams of solution), sulfuric acid (the chemical with formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H%5B2%5D ALIGN=MIDDLE  ALT=\"H%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SO%5B4%5D ALIGN=MIDDLE  ALT=\"SO%5B4%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or a solution usually containing 98 grams of that chemical per 100 grams of solution) <BR>\n" );
document.write( " <BR>\n" );
document.write( "In the language on non-chemists, it could mean a chemical that can cause burns and dissolve certain things, or LSD, or who knows what. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );