document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=710335>Question 710335</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How much of Brand A fruit punch (45 % fruit juice) must be mixed with 2 gal. of Brand B fruit punch (35% fruit juice) to create a mixture containing 43% fruit juice?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #436980 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=436980\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's analyze the problem and put everything into variables.\r<BR>\n" );
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document.write( "Low concentration L=35%<BR>\n" );
document.write( "High concentration H=45%<BR>\n" );
document.write( "Target fruit juice concentration T=43%<BR>\n" );
document.write( "Amount of low juice conc. punch  u= 2 gallons<BR>\n" );
document.write( "Amount of high conc. punch v = unknown<BR>\n" );
document.write( "Amount of punch mixture M = also unknown\r<BR>\n" );
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document.write( "Note that u+v=M.  Using this in the concentration's rational equation will be best this way.\r<BR>\n" );
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document.write( "We need this equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28uL%2BvH%29%2F%28u%2Bv%29=T ALIGN=MIDDLE  ALT=\"%28uL%2BvH%29%2F%28u%2Bv%29=T\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Our variable to solve for is v.\r<BR>\n" );
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document.write( "uL+vH=T(u+v)<BR>\n" );
document.write( "uL+vH=Tu+Tv<BR>\n" );
document.write( "vH-Tv+uL=Tu<BR>\n" );
document.write( "vH-vT=uT-uL<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28v=u%28T-L%29%2F%28H-T%29%29 ALIGN=MIDDLE  ALT=\"highlight%28v=u%28T-L%29%2F%28H-T%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, just substitute the given values into that formula for v and compute.  That will be the volume in gallons of Brand A to add to the 2 gallons of Brand B punch.  Be aware in practice you might want to know 128 fluid ounces per gallon. </SPAN>\n" );
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