document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=115235>Question 115235</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395771188/algebrahomeworkh>Algebra and trigonometry structure and method</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> how much pure antifreeze must be added to 12L of a 40% solution of antifreeze to obtain a 60% solution? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #83832 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=83832\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In 12 Liters of a 40% solution of anti-freeze there are 4.8 liters of pure anti-freeze.<BR>\n" );
document.write( "You get this by multiplying 0.4 times 12 liters.<BR>\n" );
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document.write( "You are going to add an unknown amount of pure anti-freeze to that solution. Call this unknown<BR>\n" );
document.write( "amount X. When you are done adding amount X, the total amount of anti-freeze in the solution<BR>\n" );
document.write( "will be 4.8 + X liters.<BR>\n" );
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document.write( "But when you add X liters of anti-freeze to the 12 liters of solution, the amount of solution<BR>\n" );
document.write( "also increases by the amount of X. So when you are done adding amount X, the total amount of<BR>\n" );
document.write( "solution will be 12 + X liters.<BR>\n" );
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document.write( "You want the ratio of the amount of anti-freeze in the solution to the entire amount of <BR>\n" );
document.write( "solution to be 60% or its decimal equivalent 0.6.<BR>\n" );
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document.write( "So you want 4.8 + X divided by 12 + X to equal 0.6. In equation form this is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284.8+%2B+X%29%2F%2812+%2B+X%29+=+0.6 ALIGN=MIDDLE  ALT=\"%284.8+%2B+X%29%2F%2812+%2B+X%29+=+0.6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can get rid of the denominator by multiplying both sides of the equation by (12 + X) as<BR>\n" );
document.write( "follows:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812+%2B+X%29%2A%284.8+%2B+X%29%2F%2812+%2B+X%29+=+0.6%2A%2812+%2B+X%29 ALIGN=MIDDLE  ALT=\"%2812+%2B+X%29%2A%284.8+%2B+X%29%2F%2812+%2B+X%29+=+0.6%2A%2812+%2B+X%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "On the left side, the factor (12 + X) in the numerator cancels with the factor (12 + X) in<BR>\n" );
document.write( "the denominator and you are left with:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.8+%2B+X+=+0.6%2A%2812+%2B+X%29 ALIGN=MIDDLE  ALT=\"4.8+%2B+X+=+0.6%2A%2812+%2B+X%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiply out the right side:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.8+%2B+X+=+7.2+%2B+0.6%2AX ALIGN=MIDDLE  ALT=\"4.8+%2B+X+=+7.2+%2B+0.6%2AX\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get rid of the 4.8 on the left side by subtracting 4.8 from both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X+=+2.4+%2B+0.6%2AX ALIGN=MIDDLE  ALT=\"X+=+2.4+%2B+0.6%2AX\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and get rid of the 0.6*X on the right side by subtracting 0.6*X from both sides. The result is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.4%2AX+=+2.4 ALIGN=MIDDLE  ALT=\"0.4%2AX+=+2.4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve for X by dividing both sides of this equation by 0.4 and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X+=+2.4%2F0.4+=+6 ALIGN=MIDDLE  ALT=\"X+=+2.4%2F0.4+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So if you add 6 liters of pure anti-freeze to the 12 liters of 40% solution, you end up 18 liters<BR>\n" );
document.write( "(the original 12 liters plus 6 more liters) of a 60% mixture. <BR>\n" );
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document.write( "Check this through. The original 40% solution contained 4.8 liters of anti-freeze. You<BR>\n" );
document.write( "added 6 liters of pure anti-freeze, so the new solution contains 10.8 liters of anti-freeze. <BR>\n" );
document.write( "And there now 18 liters of the new solution. Does 10.8 liters divided by 18 liters equal<BR>\n" );
document.write( "a 60% ratio? Your calculator will tell you that it does equal 0.6. So the answer checks.<BR>\n" );
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document.write( "Hope this helps you to work this problem just by thinking about what you are doing when<BR>\n" );
document.write( "you mix solutions.<BR>\n" );
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