document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=7769>Question 7769</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In order to create 3oo milliliters of a solution that is 60% alcohol, a solution that is 50% ALCOHOL is mixed with a solution that is 80% alcohol.  Ho much of each solution is required?<BR>\n" );
document.write( "__________milliliters of the 50% solution and<BR>\n" );
document.write( "__________milliliters of the 80% solution. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #4272 by </B><A HREF=/tutors/aboutme.mpl?userid=prince_abubu><B>prince_abubu(198)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=prince_abubu><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=4272\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It looks like you want to dilute (AKA, lessen/weaken) the alcohol concentration from 80% to 60% by mixing in a 50% alcohol solution.\r<BR>\n" );
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document.write( "Let x = the mL's of the 80% alcohol.\r<BR>\n" );
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document.write( "Let 300 - x = the mL's of the 50% alcohol. (We know that the mLs of the 80% mix and the 50% mix MUST equal to 300. Let's say that x is the mL's of the 80% alcohol and y is the mL's of the 50% alcohol. Then x + y = 300 because their volumes must add up to the 300 mL. Solving for y would mean getting the expression for the amount of 50% alcohol. That would be y = 300 - x.)\r<BR>\n" );
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document.write( "So, we know that there's x mL of the 80% alchol. That's the 0.8x.\r<BR>\n" );
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document.write( "We know that the 50% alcohol is (300 - x) mL, which translates to 0.5(300 - x) Since we're adding this 50% solution to the 80%, our equation so far is 0.8x + 0.5(300 - x).\r<BR>\n" );
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document.write( "After those two are combined, we should get a mixture that is 300 mL AND 60%. So, 0.8x + 0.5(300 - x) = 0.6(300). Now we're going to solve for x, the amount of 80% solution we started with.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0.8x+%2B+150+-+0.5x+=+180+ ALIGN=MIDDLE  ALT=\"+0.8x+%2B+150+-+0.5x+=+180+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---- used distributive property<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0.3x+%2B+150+=+180+ ALIGN=MIDDLE  ALT=\"+0.3x+%2B+150+=+180+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--- combined like terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0.3x+=+30+ ALIGN=MIDDLE  ALT=\"+0.3x+=+30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+100+ ALIGN=MIDDLE  ALT=\"+x+=+100+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So there were 100 mL of the 80% solution. If the entire mixture was 300 mL in total, then there would have been 200 mL of the 50% solution. </SPAN>\n" );
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