document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=25563>Question 25563</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i am not getting mixture problems so can someone help me. the question is The radiator of an automobile already contains 12 quarts of a 10% solution. How much alchohal must be added to make a mixture of 20% alcohal. How much alcohol must be added to make a mixture containing 25% alcohal. I would appreciate it so much if someone could help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #13705 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=13705\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a)---------------------------------------------------------<BR>\n" );
document.write( "This is how I see it. <BR>\n" );
document.write( "I'm starting out with 12 quarts and adding alcohol to it, so I'm going<BR>\n" );
document.write( "to end up with a little over 12 quarts of mixture with a little more than twice as much <BR>\n" );
document.write( "alcohol in it than I started.<BR>\n" );
document.write( "I'll call the amount of alcohol I need to add x.<BR>\n" );
document.write( "So, I'm going to end up with (12 + x) quarts<BR>\n" );
document.write( "How much alcohol did I have in the radiator to start with?<BR>\n" );
document.write( "I had 10% of 12 quarts, which is 1.2 quarts<BR>\n" );
document.write( "Now I can write an equation in words <BR>\n" );
document.write( "(alcohol started out with) + (alcohol to be added)<BR>\n" );
document.write( "_________________________________________________ = 20%<BR>\n" );
document.write( " (12 quarts of mixture) + (alcohol to be added)\r<BR>\n" );
document.write( "\n" );
document.write( "putting in values:<BR>\n" );
document.write( "(1.2 + x)/(12 + x) = .20<BR>\n" );
document.write( "multiply both sides by (12 + x) and expand<BR>\n" );
document.write( "1.2 + x = 2.4 + .2x<BR>\n" );
document.write( "subtract .2x from both sides<BR>\n" );
document.write( "1.2 + .8x = 2.4<BR>\n" );
document.write( "subtract 1.2 from both sides<BR>\n" );
document.write( ".8x = 1.2<BR>\n" );
document.write( "divide both sides by .8<BR>\n" );
document.write( "x = 1.5<BR>\n" );
document.write( "so, the answer is - add 1.5 quarts to make a 20% mixture<BR>\n" );
document.write( "check the answer:<BR>\n" );
document.write( "(1.2 + 1.5)/(12 + 1.5) =20%<BR>\n" );
document.write( "2.7 / 13.5 = .20<BR>\n" );
document.write( "27/135 = .20<BR>\n" );
document.write( "this is true- answer checks<BR>\n" );
document.write( "(b)--------------------------------------------------------------<BR>\n" );
document.write( "How much alcohol needs to be added to make a 25% mixture?<BR>\n" );
document.write( "If I'm starting with 12 quarts of 10% mixture, then the equation is:<BR>\n" );
document.write( "(1.2 + x) / (12 + x) = 25%<BR>\n" );
document.write( "(c)---------------------------------------------------------------<BR>\n" );
document.write( "But if I'm starting out with the 20% mixture I just made, I need to ask<BR>\n" );
document.write( "new questions<BR>\n" );
document.write( "Whats's the total amount of mixture I'm starting with?<BR>\n" );
document.write( "It's (12 + 1.5)<BR>\n" );
document.write( "What's the total amount of mixture I'm going to end up with?<BR>\n" );
document.write( "It's (12 + 1.5 + x) where x is what I have to add to get a 25% mixture<BR>\n" );
document.write( "How much alcohol am I starting out with?<BR>\n" );
document.write( "It's (1.2 + 1.5)<BR>\n" );
document.write( "How much will I end up with?<BR>\n" );
document.write( "It's (1.2 + 1.5 + x)<BR>\n" );
document.write( "So, what's my equation?<BR>\n" );
document.write( "(1.2 + 1.5 + x) / (12 + 1.5 + x) = .25<BR>\n" );
document.write( "(2.7 + x) / (13.5 + x) = .25<BR>\n" );
document.write( "multiply both sides by (13.5 + x) and expand<BR>\n" );
document.write( "2.7 + x = 3.375 + .25x <BR>\n" );
document.write( "subtract .25x from both sides<BR>\n" );
document.write( "2.7 + .75x = 3.375<BR>\n" );
document.write( "subtract 2.7 from both sides<BR>\n" );
document.write( ".75x = .675<BR>\n" );
document.write( "divide both sides by .75<BR>\n" );
document.write( "x = .9<BR>\n" );
document.write( "So, if I start with 13.5 quarts of a 20% mixture, I'll have to add .9 quarts<BR>\n" );
document.write( "to make it a 25% mixture.<BR>\n" );
document.write( "check the answer:<BR>\n" );
document.write( "(2.7 + .9)/(13.5 + .9) = .25<BR>\n" );
document.write( "3.6 / 14.4 = .25<BR>\n" );
document.write( "This is true, so answer checks<BR>\n" );
document.write( "The  (c) approach is probably what's required, because it takes a little more thought. Hope all this helps.    </SPAN>\n" );
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