document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=250511>Question 250511</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find how many quarts of 4% butterfat milk and 1% butterfat milk should be mixed to yield 90 quarts of 3% butterfat milk.\r<BR>\n" );
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document.write( "The mixture should contain __ quarts of the 4% butterfat milk.<BR>\n" );
document.write( "The mixture should contain __ quarts of the 1% butterfat milk. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #182399 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=182399\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = number of quarts at 4% butterfat.<BR>\n" );
document.write( "y = number of quarts at 1% butterfat.\r<BR>\n" );
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document.write( "you want to get 90 quarts of 3% butterfat.\r<BR>\n" );
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document.write( "amount of butterfat you get in the mixture will be .03 * 90 = 2.7 quarts of butterfat.\r<BR>\n" );
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document.write( ".04 * x + .01 * y = 2.7 (equation 1)\r<BR>\n" );
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document.write( "x + y = 90 (equation 2)\r<BR>\n" );
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document.write( "equation 1 tells you how much of x and y you need to get 2.7 quarts of butterfat.\r<BR>\n" );
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document.write( "equation 2 tells you how much of x and y you need to get 90 quarts of milk total.\r<BR>\n" );
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document.write( "you need to solve these equations simultaneously so the same value of x and y satisfies both equations.\r<BR>\n" );
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document.write( "solve for x in equation 2 to get:\r<BR>\n" );
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document.write( "x = 90 - y\r<BR>\n" );
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document.write( "substitute for x in equation 1 and solve for y.\r<BR>\n" );
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document.write( ".04 * x + .01 * y = 2.7 (equation 1) becomes:\r<BR>\n" );
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document.write( ".04 * (90-y) + .01*y = 2.7\r<BR>\n" );
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document.write( "simplify by removing parentheses to get:\r<BR>\n" );
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document.write( ".04*90 - .04*y + .01*y = 2.7\r<BR>\n" );
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document.write( "simlify by performing indicated operations and combining like terms to get\r<BR>\n" );
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document.write( "3.6 - .03y = 2.7\r<BR>\n" );
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document.write( "add .03y to both sides of the equation and subtract 2.7 from both sides of the equation to get:\r<BR>\n" );
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document.write( "3.6 - 2.7 = .03y\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( ".9 = .03y\r<BR>\n" );
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document.write( "divide both sides of the equation by .03 to get\r<BR>\n" );
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document.write( "y = 30\r<BR>\n" );
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document.write( "if y = 30, then x = 90-y = 60\r<BR>\n" );
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document.write( "x = 60<BR>\n" );
document.write( "y = 30\r<BR>\n" );
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document.write( "substitute in original equation to confirm the answer is true.\r<BR>\n" );
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document.write( "original equation is:\r<BR>\n" );
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document.write( ".04 * x + .01 * y = 2.7\r<BR>\n" );
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document.write( "substitute for x and y to get:\r<BR>\n" );
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document.write( ".04 * 60 + .01 * 30 = 2.7\r<BR>\n" );
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document.write( "this becomes 2.7 = 2.7 which is true, confirming that the answer is correct.\r<BR>\n" );
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document.write( "the answer is:\r<BR>\n" );
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document.write( "the mixture should contain 60 quarts of 4% butterfat milk.<BR>\n" );
document.write( "the mixture should contain 30 quarts of 1% butterfat milk.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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