document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=86258>Question 86258</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A researcher orders a broth of 7.5% glucose for her lab. However, she needs a stronger broth, one that is 24.9% glucose. Fortunately, she has 26.9 liters of 36.1% glucose broth in the stock room. How much 24.9% glucose broth can she make? \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 #62368 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=62368\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Let x=amount of 7.5% glucose broth that needs to be added to the 36.1% broth in order to get a 24.9% broth\r<BR>\n" );
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document.write( "Then 26.9+x=amount of 24.9% glucose broth that can be made.\r<BR>\n" );
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document.write( "Amount of pure glucose in the 7.5% broth is 0.075x<BR>\n" );
document.write( "Amount of pure glucose in the 36.1% broth is 0.361(26.9)<BR>\n" );
document.write( "Amount of pure glucose in the final broth is 0.249(26.9+x)\r<BR>\n" );
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document.write( "pure glucose before = pure glucose after\r<BR>\n" );
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document.write( "0.075x+0.361(26.9)=0.249(26.9+x)  get rid of parens\r<BR>\n" );
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document.write( "0.075x+9.7109=6.6981+0.249x  subtract 9.7109 and also 0.249x from both sides\r<BR>\n" );
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document.write( "0.075x+9.7109-9.7109-0.249x=6.6981-9.7109+0.249x-0.249x  collect like terms\r<BR>\n" );
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document.write( "-0.174x=-3.0128  divide both sides by -0.174\r<BR>\n" );
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document.write( "x=17.31 --------------------liters of 7.5% broth that's needed\r<BR>\n" );
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document.write( "26.9+17.31=44.215-------------------liters of 24.9% broth that can be made\r<BR>\n" );
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document.write( "CK\r<BR>\n" );
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document.write( "0.075(17.31)+0.361(26.9)=0.249(44.215)<BR>\n" );
document.write( "1.298+9.7109=11.009<BR>\n" );
document.write( "11.009=11.009\r<BR>\n" );
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document.write( "Hope this helps---ptaylor\r<BR>\n" );
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