document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=263512>Question 263512</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a pharmacist wants to make 150 milliliters of a 20 percent alcohol solution, but only has a 30 percent alcohol solution and a 15 percent alcohol solution, how much of each solution should she mix together to get what she needs? <BR>\n" );
document.write( "Could you please take me step by step? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #194191 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=194191\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When solving a solution problem, you have to determine how much of the 'pure' stuff you need in the solution.<BR>\n" );
document.write( "In this case, you need 150 ml of 20% alcohol.  <BR>\n" );
document.write( "That means there will be 30 ml of alcohol and 120 ml of water.<BR>\n" );
document.write( "Using the 30% solution, how much would you need to have 30 ml of pure 'alcohol'?<BR>\n" );
document.write( "30 ml = .3x<BR>\n" );
document.write( ".3x = 30<BR>\n" );
document.write( "x = 100 ml<BR>\n" );
document.write( "That is, if you have 100 ml of 30% alcohol solution, then you have 30 ml of alcohol and 70 ml of water.<BR>\n" );
document.write( "So, measure our 100 ml of the 30% alcohol solution and add 50 ml of pure water.<BR>\n" );
document.write( "You now will have a total volume of 150 ml, of which, 30 ml are pure alcohol.<BR>\n" );
document.write( "30/150 = .2 <BR>\n" );
document.write( "which means you have your required 150 ml of 20% alcohol solution.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Unless you're required to use the 15% alcohol solution, why bother with it at all?  Just dilute the 30% solution and you're done.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "But teachers can be picky... <BR>\n" );
document.write( ".<BR>\n" );
document.write( "So another way to look at the problem is to think in terms any other word problem.<BR>\n" );
document.write( "You need to mix a 30% solution and a 15% solution to arrive at a 20% solution.<BR>\n" );
document.write( "We know the final result is supposed to be 150 ml of 20% solution, which we can show as  .2*150.<BR>\n" );
document.write( "If we use 'x' amount of the 30% solution, then we are forced to use 150-x of the 15% solution.<BR>\n" );
document.write( "That defines an equation:<BR>\n" );
document.write( ".3x + .15(150-x) = .2(150)<BR>\n" );
document.write( ".3x + 22.5 - .15x = 30<BR>\n" );
document.write( ".3x - .15x = 30 - 22.5<BR>\n" );
document.write( ".15x = 7.5<BR>\n" );
document.write( "x = 50<BR>\n" );
document.write( "So you use 50 ml of the 30% solution and 150-50 = 100 ml of the 15% solution.<BR>\n" );
document.write( "Check this by determining how much 'pure stuff' is in the final solution.<BR>\n" );
document.write( ".15*100 = 15<BR>\n" );
document.write( ".3*50 = 15<BR>\n" );
document.write( "total = 30 ml of pure alcohol in the 150 ml<BR>\n" );
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