document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=242296>Question 242296</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A chef is using a mixture of two brands of Italian dressing. The first brand contains 8% vinegar, and the second brand contains 13% vinegar. The chef wants to make 320 milliliters of a dressing that is 11% vinegar. How much of each brand should she use? \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #177378 by </B><A HREF=/tutors/aboutme.mpl?userid=kelli_scofield><B>kelli_scofield(5)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=kelli_scofield><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=177378\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I am a visual learner, so I try to draw a picture to help me understand a word problem.  In a mixture problem, you are working with an amount(ml) and a concentration(%).\r<BR>\n" );
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document.write( "I draw 3 lines ___+___=___ (I usually use boxes instead of lines to combine the #'s and variables) <BR>\n" );
document.write( "Let your first brand = x<BR>\n" );
document.write( "Let your second brand = y<BR>\n" );
document.write( "You do not need a variable for the product because you have an amount and a concentration already.  Use the variables (x and y) to replace your unknowns.  The unknowns are the amounts of the first and second brands.\r<BR>\n" );
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document.write( "x+y=320 (this is your equation for the amounts)<BR>\n" );
document.write( "0.08x +0.13y=.11(320) (this is your equation for the concentrations)\r<BR>\n" );
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document.write( "We can use the substitution or elimination method to solve this.  I will use the substitution method.  I don't like using decimals, so I am going to move the decimal place two units to the right to make them whole numbers.  This gives me: 8x+13y=11(320)\r<BR>\n" );
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document.write( "Using substitution on the first equation, I put X on one side of the equation.  This gives me x=(-y+320).  I can now substitute (-y+320) for x in the second equation.\r<BR>\n" );
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document.write( "8(-y+320)+13y=3520<BR>\n" );
document.write( "-8y+2560+13y=3520<BR>\n" );
document.write( "Subtract 2560 from both sides and combine 13y and -8y.  This gives you 5y=960.  Divide both sides of the equation by 5.  This gives you y=192.\r<BR>\n" );
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document.write( "y=192<BR>\n" );
document.write( "x=128\r<BR>\n" );
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document.write( "I got x by plugging y into equation #1.<BR>\n" );
document.write( "x+(192)=320. After subtracting 192 from 320, I get x= 128.<BR>\n" );
document.write( "To check your answer, always substitute x and y in for both equations.<BR>\n" );
document.write( "ANSWER: The chef should use 128 milliliters of the 8% vinegar brand and 192 milliliters of the 13% vinegar brand. </SPAN>\n" );
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