document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=609155>Question 609155</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find how many quarts of 6% butterfat milk and 3% butterfat milk should be mixed to yield 75 quarts of 5% butter milk? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #383639 by </B><A HREF=/tutors/aboutme.mpl?userid=math-vortex><B>math-vortex(648)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math-vortex><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=math-vortex><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=383639\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, there--<BR>\n" );
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document.write( "To solve this problem we will create a system of equations modeling the information in the problem.<BR>\n" );
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document.write( "Let x be the number of quarts of 6% butterfat milk.<BR>\n" );
document.write( "Let y be the number of quarts of 3% butterfat milk.<BR>\n" );
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document.write( "6% butterfat means that six-hundredths of each quart is butterfat. Since we want to know the amount of butter fat in x quarts, we multiply, 0.06*x or just .06x.<BR>\n" );
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document.write( "Using similar reasoning, the amount of butterfat in the 3% butterfat milk would be .03y.<BR>\n" );
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document.write( "We want to end up with 75 quarts of 5% butterfat milk. Five-hundredths of each of these quarts is butterfat and we have 75 quarts so we multiply again. There are (.05)(75)=3.75 quarts of butterfat in the final 75 quarts.<BR>\n" );
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document.write( "We can use this information to write an equation:<BR>\n" );
document.write( "[the butterfat in the 6% milk] + [the butterfat in the 3% milk] = [butterfat in the final product]<BR>\n" );
document.write( "0.06x + 0.03y = 3.75<BR>\n" );
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document.write( "We can write a second equation about the total volume of the milk:<BR>\n" );
document.write( "[the amount of 6% milk] + [the amount of 3% milk] = [amount of 5% milk]<BR>\n" );
document.write( "x + y = 75<BR>\n" );
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document.write( "Now we have two equations with two unknowns. We can solve using substitution. Set the second equation equal to y.<BR>\n" );
document.write( "x + y = 75<BR>\n" );
document.write( "y = 75 - x<BR>\n" );
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document.write( "Substitute 75 - x for y in the first equation.<BR>\n" );
document.write( "0.06x + 0.03y = 3.75<BR>\n" );
document.write( "0.06x + 0.03(75 - x) = 3.75<BR>\n" );
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document.write( "Simplify and solve for x.<BR>\n" );
document.write( "0.06x + 2.25 - 0.03x = 3.75<BR>\n" );
document.write( "0.03x +2.25 = 3.75<BR>\n" );
document.write( "0.03x = 1.50<BR>\n" );
document.write( "x = 50<BR>\n" );
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document.write( "Solve for y using the second equation.<BR>\n" );
document.write( "x + y = 75<BR>\n" );
document.write( "50 + y = 75<BR>\n" );
document.write( "y = 25<BR>\n" );
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document.write( "There are 50 quarts of 6% butterfat milk and 25 quarts of 3% butterfat milk.<BR>\n" );
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document.write( "We can check our work by making use the amount of butterfat is correct:<BR>\n" );
document.write( ".06(50) = 3 quarts of butterfat from the 6% solution.<BR>\n" );
document.write( ".03(25) = 0.75 quarts of butterfat from the 3% solution.<BR>\n" );
document.write( "Together, we have 3.75 quarts of butterfat.<BR>\n" );
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document.write( "Check!<BR>\n" );
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document.write( "Hope this helps. Feel free to email me via gmail if you have questions about the solution.<BR>\n" );
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document.write( "Ms.Figgy<BR>\n" );
document.write( "math.in.the.vortex@gmail.com<BR>\n" );
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