document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1195943>Question 1195943</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ethanol fuel mixtures have \"E\" numbers that indicate the percentage of ethanol in the mixture by volume. For example, E10 is a mixture of 10%ethanol and 90% gasoline. How much E5 should be mixed with 4000gal of E10to make an E9 mixture?<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 #828579 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=828579\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The typical algebraic setup for solving the problem would look something like this:<br><BR>\n" );
document.write( "4000 gallons of 10% ethanol, plus x gallons of 5% ethanol, yields (4000+x) gallons of 9% ethanol<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.10%284000%29%2B.05%28x%29=.09%284000%2Bx%29 ALIGN=MIDDLE  ALT=\".10%284000%29%2B.05%28x%29=.09%284000%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "I'll leave it to you to find the answer by that method.<br><BR>\n" );
document.write( "Here is another very different way to solve any 2-part mixture problem like this which, if the numbers are \"nice\", gets you to the answer faster and with less work.<br><BR>\n" );
document.write( "You are mixing 5% and 10% ethanol to get a mixture that is 9% ethanol.<BR>\n" );
document.write( "Consider the three percentages on a number line: 5, 9, 10.<BR>\n" );
document.write( "Observe/calculate that 9% is 4/5 of the way from 5% to 10%.<BR>\n" );
document.write( "That means 4/5 of the mixture must be the 10% ethanol, so 1/5 of the mixture is the 5% ethanol; that means the amount of 5% ethanol must be 1/4 the amount of 10% ethanol.<br><BR>\n" );
document.write( "There are 4000 gallons of the 10% ethanol, so the number of gallons of the 5% ethanol must be (1/4)(4000) = 1000.<br><BR>\n" );
document.write( "ANSWER: 1000 gallons<br><BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( ".10(4000)+.05(1000)=400+50 = 450<BR>\n" );
document.write( ".09(5000) = 450<br><BR>\n" );
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