document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1094740>Question 1094740</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a laboratory needs to make a 21-liter batch of a 40% acid solution. how can the laboratory technician combine a batch of an acid solution that is pure acid with another that is 10% to get 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 #709312 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=709312\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>First, here is an easy way to solve mixture problems like this, if you can understand it....<br><BR>\n" );
document.write( "(1) Look to see how far (or close) the percentage of the mixture is to the percentages of the two ingredients:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100-40+=+60 ALIGN=MIDDLE  ALT=\"100-40+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40-10+=+30 ALIGN=MIDDLE  ALT=\"40-10+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The percentage of the mixture, 40%, is \"twice as close\" to 10% as it is to 100%.  That means there must be twice as much of the 10% ingredient as the 100% ingredient.  So 2/3 of the mixture must be the 10% acid solution, and 1/3 must be the pure (100%) acid.<br><BR>\n" );
document.write( "2/3 of the 21 liters is 14 liters; so you need 14 liters of the 10% acid solution and 7 liters of pure acid.<br><BR>\n" );
document.write( "If you want to use the slow traditional algebraic solution method...<br><BR>\n" );
document.write( "let x = liters of 10% acid solution<BR>\n" );
document.write( "then 21-x = liters of pure (100%) acid<br><BR>\n" );
document.write( "The total mixture is 21 liters; the amount of acid is 10% of the x, plus 100% of the (21-x).  You want the amount of acid to be 40% of the total mixture, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.10%28x%29%2B1%2821-x%29+=+.40%2821%29 ALIGN=MIDDLE  ALT=\".10%28x%29%2B1%2821-x%29+=+.40%2821%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.1x+%2B+21-x+=+8.4 ALIGN=MIDDLE  ALT=\".1x+%2B+21-x+=+8.4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12.6+=+.9x ALIGN=MIDDLE  ALT=\"12.6+=+.9x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14+=+x ALIGN=MIDDLE  ALT=\"14+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "liters of the 10% acid solution: x = 14<BR>\n" );
document.write( "liters of pure (100%) acid: 21-x = 7<BR>\n" );
document.write( " </SPAN>\n" );
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