document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=250615>Question 250615</A>: <I><SPAN STYLE=\"word-break: break-all;\">  The sterilization tank contains 100 gallons 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( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #184989 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=184989\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> we have 100 gallons of 2% bleach\r<BR>\n" );
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document.write( "we need 100 gallon of 5% bleach.\r<BR>\n" );
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document.write( "100 * .02 = 2 gallons of bleach in the original mixture.\r<BR>\n" );
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document.write( "we need 100 * .05 = 5 gallons of bleach in the new mixture.\r<BR>\n" );
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document.write( "let x represent the number of gallons that have to be replaced.\r<BR>\n" );
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document.write( "we want to have 5 gallons in the new mixture.\r<BR>\n" );
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document.write( "we have 2 gallons in the original mixture.\r<BR>\n" );
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document.write( "we will need to add x gallons of pure bleach.\r<BR>\n" );
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document.write( "in the process we will be removing .02*x gallons of bleach from the original mixture.\r<BR>\n" );
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document.write( "the formula becomes:\r<BR>\n" );
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document.write( "5 = 2 - .02*x + x\r<BR>\n" );
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document.write( "where:\r<BR>\n" );
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document.write( "5 is the number of gallons of bleach we want in the new mixture.<BR>\n" );
document.write( "2 is the number of gallons of bleach in the original mixture.<BR>\n" );
document.write( "x is the number of gallons of pure bleach we will be adding.<BR>\n" );
document.write( ".02*x is the number of gallons of pure bleach we will be removing.\r<BR>\n" );
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document.write( "the formula simplifies to:\r<BR>\n" );
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document.write( "5 = 2 + .98x\r<BR>\n" );
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document.write( "subtract 2 from both sides of this equation to get:\r<BR>\n" );
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document.write( "3 = .98x\r<BR>\n" );
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document.write( "divide both sides of this equation by .98 to get:\r<BR>\n" );
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document.write( "x = 3/.98 = 3.06122449\r<BR>\n" );
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document.write( "they need to replace 3.06122449 gallons of a 2% mixture with 3.06122449 gallons of pure bleach to reach the required concentration.\r<BR>\n" );
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document.write( "assume they remove 3.06122449 gallons of the 2% mixture.\r<BR>\n" );
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document.write( "they now have 96.93877551 gallons of 2% mixture.\r<BR>\n" );
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document.write( "this means they have .02 * 96.93877551 = 1.93877551 gallons of bleach.\r<BR>\n" );
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document.write( "they add 3.06122449 gallons of pure bleach.\r<BR>\n" );
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document.write( "their total gallons becomes 96.93877551 + 3.06122449 = 100 gallons.\r<BR>\n" );
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document.write( "their bleach content becomes 1.93877551 + 3.06122449 = 5 gallons.\r<BR>\n" );
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document.write( "they now have a 5% solution.\r<BR>\n" );
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document.write( "they needed to replace 3.06122449 gallons of the 2% mixture with 3.06122449 gallons of pure bleach.\r<BR>\n" );
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