document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=243494>Question 243494</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how much pure acid should be mixed with 9 gallons of a 50% acid solution in order to get an 80% acid solution </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #178389 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=178389\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Always start by sorting out what you know and assigning variables.  We know we have 9 gallons of 50% acid solution. Multiplying 9 by .5 = 4.5 gallons of pure acid in the solution.<BR>\n" );
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document.write( "We need to know how much more pure acid we need to add  to get an 80% acid solution.<BR>\n" );
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document.write( "Set the unknown to x.<BR>\n" );
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document.write( "Since we are adding x gallons of pure acid, the final solution will be 9+x gallons at 80% acid.  We can state this algebraically as:  .8(9+x)<BR>\n" );
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document.write( "It will consist of 9 gallows of .5 acid solution + x gallons of 100% acid.  We can show this as<BR>\n" );
document.write( ".5(9) + 1(x)<BR>\n" );
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document.write( "Of course, we don't normally show 1 times anything. But I just wanted to be clear.<BR>\n" );
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document.write( "Combining we have:<BR>\n" );
document.write( ".8(9+x) = .5(9) + x<BR>\n" );
document.write( "Multiplying what we have in parentheses<BR>\n" );
document.write( "7.2 + .8x = 4.5 + x<BR>\n" );
document.write( "Subtracting 4.5 from both sides<BR>\n" );
document.write( "2.7 + .8x = x<BR>\n" );
document.write( "Subtracting .8x from both sides<BR>\n" );
document.write( "2.7 = .2x<BR>\n" );
document.write( "Dividing both sides by .2<BR>\n" );
document.write( "13.5 = x<BR>\n" );
document.write( "x = 13.5<BR>\n" );
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document.write( "So this suggests we need to add 13.5 gallons of pure acid to get to an 80% solution.<BR>\n" );
document.write( "That seems like an awful lot.  But we always check our work, so that's next anyway.<BR>\n" );
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document.write( "If we add 13.5 gallons to 9 gallons, we have 22.5 gallons of solution in total.<BR>\n" );
document.write( "If it is 80% acid, then we would have .8(22.5) = 18 gallons of pure acid in the solution.<BR>\n" );
document.write( "We started with 4.5 gallons of pure acid and added 13.5 gallons of pure acid = 18.<BR>\n" );
document.write( "Done. </SPAN>\n" );
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