document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=511529>Question 511529</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What quantity of a 60% acid solution must be mixed with a 20% solution to produce 200 mL of a 55% solution?\r<BR>\n" );
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document.write( "I don't know what to try, everything the book has to say on this problem provides no help what-so-ever. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #342247 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=342247\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Keep track of how much 'pure' stuff you need.<BR>\n" );
document.write( "You need 200 mL of a 55% solution, so you need<BR>\n" );
document.write( ".55*200 = 110 mL of 'pure' acid and 90 mL of water (or other stuff).<BR>\n" );
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document.write( "You need to mix two solutions to arrive a defined total volume, so you need to state the two amounts in terms of one unknown.<BR>\n" );
document.write( "x mL of 60% acid<BR>\n" );
document.write( "200-x mL of 20% acid<BR>\n" );
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document.write( "60%(x) + 20%(200-x) = 110 mL<BR>\n" );
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document.write( ".6x + .2(200-x) = 110<BR>\n" );
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document.write( "multiply by 10 to eliminate decimal.<BR>\n" );
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document.write( "6x + 2(200-x) = 1100<BR>\n" );
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document.write( "6x + 400 -2x = 1100<BR>\n" );
document.write( "4x = 700<BR>\n" );
document.write( "x = 700/4<BR>\n" );
document.write( "x = 175<BR>\n" );
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document.write( "200-x = 25<BR>\n" );
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document.write( "So this suggests you need:<BR>\n" );
document.write( "175 mL of 60% solution<BR>\n" );
document.write( "25 mL of 20% solution<BR>\n" );
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document.write( "Calculate the total 'pure' acid to see if this answer is correct.<BR>\n" );
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document.write( ".6*175 = 105 mL<BR>\n" );
document.write( ".2*25 = 5 mL<BR>\n" );
document.write( "105 + 5 = 110 mL<BR>\n" );
document.write( "which is exactly how much pure acid you needed in the 200 mL for it to be 55% solution.<BR>\n" );
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document.write( "Answer:  Mix 175 mL of 60% acid with 25 mL of 20% acid to make 200 mL of 55% acid.<BR>\n" );
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document.write( "Done. </SPAN>\n" );
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