document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=251464>Question 251464</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mixture A is 7.5% acid. To raise the concentration of acid to 10%, some pure acid will be added to the mixture. How many liters of mixture A and how many liters of pure acid are needed to end up with 200 liters of 10% solution.\r<BR>\n" );
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document.write( "Not sure if I started it out right, that's why I'm here!\r<BR>\n" );
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document.write( "x = pure acid<BR>\n" );
document.write( "A = Mixture A\r<BR>\n" );
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document.write( "7.5 + x = (200)(.10) x = 12.5 liters\r<BR>\n" );
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document.write( "If that's right, I'm not sure where to go from there. If you can help me, that would be great! Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #183147 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=183147\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mixture A is 7.5% acid.\r<BR>\n" );
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document.write( "let x = amount of mixture A.\r<BR>\n" );
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document.write( "7.5% of x is equivalent to .075 * x (you have to divide percent by 100% to get proportion).\r<BR>\n" );
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document.write( "this means that .075 * x = amount of acid in mixture A.\r<BR>\n" );
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document.write( "let y = amount of mixture C.\r<BR>\n" );
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document.write( "then 1.0 * y = amount of acid in mixture B.\r<BR>\n" );
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document.write( "this is because 100% of mixture B is equivalent to 1.0 * mixture B.\r<BR>\n" );
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document.write( "mixture C is equal to 200 liters.\r<BR>\n" );
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document.write( "this means that:\r<BR>\n" );
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document.write( "x + y = 200\r<BR>\n" );
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document.write( "mixture C will contain 10% acid which means that mixture C will contain .10 * 200 = 20 liters of acid.\r<BR>\n" );
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document.write( "this means that:\r<BR>\n" );
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document.write( ".075 * x + y = 20\r<BR>\n" );
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document.write( "you have 2 equations that need to be solved simultaneously.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "x + y = 200 (first equation)\r<BR>\n" );
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document.write( ".075*x + y = 20 (second equation)\r<BR>\n" );
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document.write( "you can solve for y in either equation and then solve for x in the other equation.\r<BR>\n" );
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document.write( "we'll solve for y in the first equation to get:\r<BR>\n" );
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document.write( "y = 200-x\r<BR>\n" );
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document.write( "we'll substitute for y in the second equation to get:\r<BR>\n" );
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document.write( ".075*x + (200-x) = 20\r<BR>\n" );
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document.write( "remove parentheses to get:\r<BR>\n" );
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document.write( ".075*x + 200 - x = 20\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "-.925*x + 200 = 20\r<BR>\n" );
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document.write( "subtract 200 from both sides to get:\r<BR>\n" );
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document.write( "-.925*x = 20-100 = -180\r<BR>\n" );
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document.write( "divide both sides by -.925 to get:\r<BR>\n" );
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document.write( "x = -180 / -.925 = 194.5945946\r<BR>\n" );
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document.write( "use this value of x to solve for y in the first equation to get:\r<BR>\n" );
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document.write( "y = 200 - 194.5945946 = 5.405405405\r<BR>\n" );
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document.write( "use the values for x and y in the second equation to confirm that they are good.\r<BR>\n" );
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document.write( "the second equation is:\r<BR>\n" );
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document.write( ".075*x + y = 20\r<BR>\n" );
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document.write( "substituting for x and y in that equation, we get:\r<BR>\n" );
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document.write( ".075*194.5945946 + 5.405405405 = 20\r<BR>\n" );
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document.write( "this becomes 20 = 20 which is true confirming our values for x and y are good.\r<BR>\n" );
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document.write( "your answer is:\r<BR>\n" );
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document.write( "you need to add 5.405405405 liters of pure acid to make a 200 liter mixture of 10% acid.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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