document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=945690>Question 945690</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please show me the way you solve this problem. i am almost there. How many gallons of 5% acid solution should be mixed with 20 gallons of a 10% acid solution to obtain an 8% acid solution?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #576852 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=576852\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A CHEMIST\"S NOTE: Be careful with acids. Do not use them or mix them unless you know exactly what they are, and what will or may happen when you mix them.<BR>\n" );
document.write( "I have tablets that are mostly ascorbic acid (vitamin C) an others that are almost pure acetylsalicilic acid (aspirin) in the medicine cabinet section of my kitchen at home. Most people can swallow one of those tablets without ill effects.<BR>\n" );
document.write( "In the lab, in a vented cabinet under the fume hood, I have liquids labeled sulfuric acid, nitric acid, glacial acetic acid, trifluoroacetic acid, and hydrochloric acid. The last one is a 36%w/w solution of hydrogen chloride gas in water. Do not ingest those.<BR>\n" );
document.write( "I also have a lot of solids in my lab shelves with labeled names that include the word acid. The labels tell you about their dangers. <BR>\n" );
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document.write( "According to math teachers who never learned enough chemistry:<BR>\n" );
document.write( "1) \"Acid\" is a term that is descriptive enough.<BR>\n" );
document.write( "2) \"A 10% solution\" is a phrase with an unequivocal meaning.<BR>\n" );
document.write( "3) When you mix volumes of liquids, the volume of the resulting mixture is the sum of the volumes mixed.<BR>\n" );
document.write( "In the real world, none of that is true, but in the math teachers' world it works just fine.<BR>\n" );
document.write( "In both worlds, we all agree that the amount of \"acid\" in the mixture is the sum of the amounts of \"acid\" that were in the solutions that were mixed.<BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >= gallons of 5% acid solution that we need to mix with 20 gallons of a 10% acid solution to obtain an 8% acid solution.<BR>\n" );
document.write( "Your teacher believes that 100 gallons an \"8% solution of acid\" contains 8 gallons of some liquid called \"acid\". I would describe that solution as an 8% (v/v) solution, where the \"(v/v)\" means volume in volume.<BR>\n" );
document.write( "Your teacher believes that 100 gallons a \"5% solution of acid\" contains 5 gallons of some liquid called \"acid\". So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > gallons of that solution contain <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2F100=0.05x ALIGN=MIDDLE  ALT=\"5x%2F100=0.05x\"   DISABLED_style= \"max-width:90%; height:auto;\" > gallons of acid.<BR>\n" );
document.write( "Your teacher also believes that 100 gallons a \"10% solution of acid\" contains 10 gallons of some liquid called \"acid\".  So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20 ALIGN=MIDDLE  ALT=\"20\"   DISABLED_style= \"max-width:90%; height:auto;\" > gallons of that solution contain <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2A10%2F100=2 ALIGN=MIDDLE  ALT=\"20%2A10%2F100=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > gallons of \"acid\".<BR>\n" );
document.write( "When you mix something containing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > gallons of acid with something containing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.05x ALIGN=MIDDLE  ALT=\"0.05x\"   DISABLED_style= \"max-width:90%; height:auto;\" > gallons of acid,<BR>\n" );
document.write( "you get a mixture containing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%280.05x%2B2%29%7D%7D+gallons+of+%22acid%22.%0D%0AYour+teacher+believes+that+the+total+volume+the+mixture+will+the+sum+of+the+volumes+mixed%2C%0D%0A%7B%7B%7B20%2Bx ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > gallons,<BR>\n" );
document.write( "That mixture is expected to be an \"8% solution of acid\", and<BR>\n" );
document.write( "since your teacher believes that 100 gallons an \"8% solution of acid\" contains 8 gallons of some liquid called \"acid\",<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2Bx ALIGN=MIDDLE  ALT=\"20%2Bx\"   DISABLED_style= \"max-width:90%; height:auto;\" > gallons of that solution contain<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820%2Bx%29%2A8%2F100=red%280.08%2820%2Bx%29%29 ALIGN=MIDDLE  ALT=\"%2820%2Bx%29%2A8%2F100=red%280.08%2820%2Bx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > gallons of \"acid\".<BR>\n" );
document.write( "So our equation is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%280.08%2820%2Bx%29%29=green%280.05x%2B2%29%7D%7D%0D%0A%7B%7B%7B0.08%2A20%2B0.08x=0.05x%2B2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.6%2B0.08x=0.05x%2B2 ALIGN=MIDDLE  ALT=\"1.6%2B0.08x=0.05x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.08x-0.05x=2-1.6 ALIGN=MIDDLE  ALT=\"0.08x-0.05x=2-1.6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.08-0.05%29x=0.4 ALIGN=MIDDLE  ALT=\"%280.08-0.05%29x=0.4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.03x=0.4 ALIGN=MIDDLE  ALT=\"0.03x=0.4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0.4%2F0.03 ALIGN=MIDDLE  ALT=\"x=0.4%2F0.03\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=13.3%29 ALIGN=MIDDLE  ALT=\"highlight%28x=13.3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > gallons (rounded). </SPAN>\n" );
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