document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=619960>Question 619960</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how many liters each of a 65% acid solution and a 30% acid solution must be used to make 70 liters of 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 #389867 by </B><A HREF=/tutors/aboutme.mpl?userid=dragonwalker><B>dragonwalker(73)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=dragonwalker><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=389867\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You first want to look at each solution's difference from the desired concentration so:\r<BR>\n" );
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document.write( "for the 65% acid solution this is +5 different from the desired 60%<BR>\n" );
document.write( "for the 30% acid solution this is -30 different from the desired 60%\r<BR>\n" );
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document.write( "So in order for this to balance look at the one that has a bigger difference, in this case the 30% with a difference of -30\r<BR>\n" );
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document.write( "the difference of the 65% acid solution is only +5 so how many times is this smaller than the other difference of 30? 30/5 =6\r<BR>\n" );
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document.write( "So for every one unit of the 30% solution you need to add 6 units of the solution that makes less of a difference (65%).  This evens the changes out. To find out how much of each you know that we will be adding 6 times the 65% solution than the 30% solution so let us word it like this:\r<BR>\n" );
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document.write( "amount of 30% + amount of 65% = the total volume\r<BR>\n" );
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document.write( "we know the total volume will be 70 liters and we shall call the amount of 30% solution added 'x'\r<BR>\n" );
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document.write( "So:<BR>\n" );
document.write( "x + 6x = 70\r<BR>\n" );
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document.write( "(as if x of 30% sol. we know that six times this i.e. 6x of the 65% sol. is used)\r<BR>\n" );
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document.write( "So:<BR>\n" );
document.write( "solve for x\r<BR>\n" );
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document.write( "7x = 70\r<BR>\n" );
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document.write( "divide both sides by 7 to find x:\r<BR>\n" );
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document.write( "7x/7 = 70/7<BR>\n" );
document.write( "x = 10\r<BR>\n" );
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document.write( "so we know that 10 liters of 30% solution is needed. Therefore 6 times this amount (i.e. 60 liters) of 65% solution is also needed.\r<BR>\n" );
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document.write( "To check add these volumes together = 10+60 = 70!!! </SPAN>\n" );
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