document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=220184>Question 220184</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how much pure acid should be mixed with 3 gallons of a 20% solution in order to get a 60% 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 #165362 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=165362\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let S = amount of new solution<BR>\n" );
document.write( "Then .6*S = the amount of acid in the new solution.<BR>\n" );
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document.write( "Amount of Acid in existing 3 gallon solution is equal to .2 * 3 = .6 gallons of acid.<BR>\n" );
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document.write( "Let X be the amount of acid We need to add to the existing solution.<BR>\n" );
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document.write( "The new solution is equal to the old solution plus X because we are adding pure acid which is represented by X.<BR>\n" );
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document.write( "This means that S = X + 3<BR>\n" );
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document.write( "The amount of acid in the existing solution is .6 gallons<BR>\n" );
document.write( "We will be adding X gallons of acid.<BR>\n" );
document.write( "The Total amount of acid in the new Solution will be X + .6<BR>\n" );
document.write( "That will equal to 60% of the new solution which equals .6*S<BR>\n" );
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document.write( "This means that (X+.6) = .6*S<BR>\n" );
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document.write( "Since we know that S = (X+3), we can susbtitute in our equation to get:<BR>\n" );
document.write( "(X+.6) = .6*(X+3)<BR>\n" );
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document.write( "This reduces one equation in two unknown into one equation in one unknown which we can then solve.<BR>\n" );
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document.write( "We remove parentheses to get:<BR>\n" );
document.write( "X + .6 = .6*X + .6*3<BR>\n" );
document.write( "We Subtract .6 from both sides of the equation and we simplify to get:<BR>\n" );
document.write( "X = .6*X + .6*3 - .6 which becomes:<BR>\n" );
document.write( "X = .6*X + 1.2<BR>\n" );
document.write( "We subtract .6*X from both sides of this equation to get:<BR>\n" );
document.write( "X - .6*X = 1.2 which simplifies to:<BR>\n" );
document.write( ".4*X = 1.2<BR>\n" );
document.write( "We divide both sides of this equation by .4 to get:<BR>\n" );
document.write( "X = 1.2/.4 = 3<BR>\n" );
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document.write( "Answer is you have to add 3 gallons of acid to 3 gallons of 20% acid to get a solution that is 60% acid.<BR>\n" );
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document.write( ".6 gallons of acid in the original mixture + 3 gallons of acid = 3.6 gallons in the new mixture.<BR>\n" );
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document.write( "3 gallons of the original mixture + 3 gallons of of acid = 6 gallons of the new mixture.<BR>\n" );
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document.write( "3.6 / 6 = .6 * 100% = 60% of acid in the new mixture.\r<BR>\n" );
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