document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=272568>Question 272568</A>: <I><SPAN STYLE=\"word-break: break-all;\"> in a chemistry class, a 4% silver iodide solution must be mixed with a 10% solution to get 12 liters of a 6% solution. how many liters of the 10% solution are needed? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #199335 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=199335\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solution problems are solved most easily by keeping track of the amount of 'pure' stuff in the constituent solutions and in the final solution.<BR>\n" );
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document.write( "Here you want 12 liters of a 6% solution of silver iodide. <BR>\n" );
document.write( "That means you need .06*12 = .72 liters of 'pure' silver iodide.<BR>\n" );
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document.write( "You have a 4% and a 10% solution to add together.<BR>\n" );
document.write( "'x' can be used to indicate the amount of 4% solution.<BR>\n" );
document.write( "We could say 'y' is the amount of 10% solution, but it is likely easier to indicate '12-x' as the amount of 10% solution.<BR>\n" );
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document.write( "We can now setup the equation to be solved:<BR>\n" );
document.write( ".04x + .10y = .72<BR>\n" );
document.write( "or<BR>\n" );
document.write( ".04x + .10(12-x) = .72<BR>\n" );
document.write( ".04x + 1.2 - .1x = .72<BR>\n" );
document.write( "-.06x = -.48<BR>\n" );
document.write( "x = 8<BR>\n" );
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document.write( "y = 12-8 = 4<BR>\n" );
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document.write( "So, our candidates are:<BR>\n" );
document.write( "x = 8 liters of 4% solution<BR>\n" );
document.write( "y = 4 liters of 10% solution<BR>\n" );
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document.write( "But we have to check to know if that's right...always...<BR>\n" );
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document.write( "How much silver iodide is there in 8 liters of 4% solution?<BR>\n" );
document.write( ".04*8 = .32 liters<BR>\n" );
document.write( "How much silver iodide is there in 4 liters of 10% solution?<BR>\n" );
document.write( ".1*4 = .4 liters<BR>\n" );
document.write( "Total = .72 liters of silver iodide<BR>\n" );
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document.write( "That matches what we determined we needed initially.<BR>\n" );
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document.write( "Checking the question, we can see the answer is only \"how many liters of the 10% solution\"? 4 liters </SPAN>\n" );
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