document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=283738>Question 283738</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help with this problem a 10% acid solution is to be mixed with a 50% acid solution in order to get 120 ml of  a 20% acid solution. how many ml of the 10% solution and 50% should be mixed? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #205920 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=205920\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> With solution problems, you need to keep track of the amount of 'pure' stuff.<BR>\n" );
document.write( "You need to end up with 120 ml of a 20% solution, so that is<BR>\n" );
document.write( ".20 * 120 = 24 ml of 'pure' acid<BR>\n" );
document.write( "120-24 = 96 ml of water<BR>\n" );
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document.write( "x = volume of 10% acid <BR>\n" );
document.write( "y = volume of 50% acid<BR>\n" );
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document.write( "x+y = 120 ml<BR>\n" );
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document.write( "It is better to set up the equation with the minimum number of unknowns.<BR>\n" );
document.write( "In this case, we know the 120 ml is required, so we can say:<BR>\n" );
document.write( "x = volume of 10% acid<BR>\n" );
document.write( "120-x = volume of 50% acid<BR>\n" );
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document.write( ".1*x + .5(120-x) = .2*120<BR>\n" );
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document.write( "multiply both sides of the equation by 10 to get rid of decimals<BR>\n" );
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document.write( "10*(.1*x + .5(120-x)) = 10*(.2*120)<BR>\n" );
document.write( "10*(.1*x) + 10(.5(120-x)) = 10*(.2*120)<BR>\n" );
document.write( "x + 5(120-x) = 2*120<BR>\n" );
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document.write( "x + 600 -5x = 240<BR>\n" );
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document.write( "-4x = -360<BR>\n" );
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document.write( "x = 90<BR>\n" );
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document.write( "y = 120-90 = 30<BR>\n" );
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document.write( "Checking, how much 'pure' stuff we would have...<BR>\n" );
document.write( ".1*90 =  9 ml<BR>\n" );
document.write( ".5*30 = 15 ml<BR>\n" );
document.write( "9+15 = 24 ml, which is what we needed<BR>\n" );
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document.write( "So the answer is:<BR>\n" );
document.write( "90 ml of a 10% solution<BR>\n" );
document.write( "plus 30 ml of a 50% solution<BR>\n" );
document.write( "to produce 120 ml of 20% solution.<BR>\n" );
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document.write( "Done </SPAN>\n" );
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