document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=505697>Question 505697</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My algebra 2 question on my homework worksheet is this:\r<BR>\n" );
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document.write( "\"A health clinic uses a solution of bleach to sterilize Petri dishes in which cultures are grown. The sterilization tank contains 100 gal of a solution of 2% ordinary household bleach mixed with pure distilled water. New research indicates that the concentration of bleach should be 5% for complete sterilization. How much of the solution should be drained and replaced with bleach to increase the bleach content to the recommended level?\"\r<BR>\n" );
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document.write( "How would you solve that? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #339948 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=339948\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> With mixture problems you always have to keep track of how much 'pure' stuff you have.<BR>\n" );
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document.write( "At present you have 100 gal of 2% solution.<BR>\n" );
document.write( "2%(100) = .02*100 = 2 gallons of pure bleach added to 98 gallons of water.<BR>\n" );
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document.write( "What you need is 5 gallons of bleach added to 95 gallons of water.<BR>\n" );
document.write( "But you cannot do that because you have a tank full.<BR>\n" );
document.write( "So, you have to drain the same amount of solution as you add.<BR>\n" );
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document.write( "Let 'x' be the amount you add, which = the amount you drain.<BR>\n" );
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document.write( "2%(100) + 100%(x) - 2%(x) = 5%(100)<BR>\n" );
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document.write( ".02(100) + 1(x) - .02(x) = .05(100)<BR>\n" );
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document.write( "2 + x - .02x = 5<BR>\n" );
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document.write( ".98x = 3<BR>\n" );
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document.write( "98x = 300<BR>\n" );
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document.write( "x = 300/98<BR>\n" );
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document.write( "x = 3.0612<BR>\n" );
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document.write( "Always check your solution to see if it is truly the answer.<BR>\n" );
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document.write( "You plan to drain 3.06 gallons of the 2% solution and add 3.06 gallons of pure bleach.<BR>\n" );
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document.write( "Would that be a 5% solution?<BR>\n" );
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document.write( "The amount you drain would take some of the pure stuff with it.<BR>\n" );
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document.write( ".02*(3.0612) = .0612 gal of pure stuff would be removed from the 2.0 gallons you had in total.<BR>\n" );
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document.write( "So you would still have 1.9388 gal of pure stuff in the tank.<BR>\n" );
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document.write( "Then you add 3.0612 gallons of pure stuff, which fills the tank again.<BR>\n" );
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document.write( "1.9388 + 3.0612 = 5 gallons of pure stuff in the 100 gal tank.<BR>\n" );
document.write( "That's a 5% solution.<BR>\n" );
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document.write( "Answer:<BR>\n" );
document.write( "Drain 3.0612 of 2% solution from the 100 gallon tank and add 3.0612 gallons of pure bleach to produce 100 gallons of 5% solution.<BR>\n" );
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document.write( "Done. </SPAN>\n" );
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