document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=708854>Question 708854</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A new automobile engine can run on a mixture of gasoline and a substitute fuel. If gas costs $2.48 per gallon and the substitute fuel cost $1.82 per gallon, what percent of a mixture must be a substitute fuel to bring down to $2.15 per gallon? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #436294 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=436294\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \"What percent of the mixture\", means for 100 parts.  First set up the cost equation.\r<BR>\n" );
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document.write( "x and y, the gallons or just parts of each fuel to mix.  x the fuel, y the substitute.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.48x%2B1.82y=2.15 ALIGN=MIDDLE  ALT=\"2.48x%2B1.82y=2.15\"   DISABLED_style= \"max-width:90%; height:auto;\" > dollars  (so this uses x and y as gallons).  That is for 1 gallon of mixture.\r<BR>\n" );
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document.write( "Since that was for just 1 gallon, we expect x+y=1.  You can imagine the 1 as made of 100 equal parts; the gallon can be understood as divisible into 0.01 multiplied by 100.\r<BR>\n" );
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document.write( "We just have this system:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.48x%2B1.82y=2.15 ALIGN=MIDDLE  ALT=\"2.48x%2B1.82y=2.15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=1 ALIGN=MIDDLE  ALT=\"x%2By=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply the second equation by 1.82, and subtract it from the first equation and get a value for x (after a little more arithmetic).\r<BR>\n" );
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document.write( "2.48x-1.82x+1.82y-1.82y=2.15-1.82(1)<BR>\n" );
document.write( "0.66x=0.33<BR>\n" );
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document.write( "That means y is also <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%280.5%29 ALIGN=MIDDLE  ALT=\"highlight%280.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "ANSWER: Half gallon for each one to make 1 gallon of fuel mixture at 2.15 dollars per gallon.  50% of each fuel.\r<BR>\n" );
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