document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=104438>Question 104438</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0495012661/algebrahomeworkh>College Algebra</A><BR>\n" );
document.write( ": <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 $1.50 per gallon and the substitute fuel costs 40 cents per gallon, what percent of a mixture must be substitute fuel to bring the cost down to $1.00 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 #76031 by </B><A HREF=/tutors/aboutme.mpl?userid=stormy><B>stormy(4)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stormy><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=76031\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let g = the number of gallons of gas and s = the number of gallons of substitute fuel in the mixture.  Then:\r<BR>\n" );
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document.write( "The price of g gallons of gas = 1.50 g<BR>\n" );
document.write( "The price of s gallons of substitute fuel = 0.40 s\r<BR>\n" );
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document.write( "Therefore, the price of the mixture is: 1.50 g + 0.40 s\r<BR>\n" );
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document.write( "To get a price of 1.00 per gallon, you have to mix the two types.  The price of this mixture is $1 multiplied the total number of gallons in the mixture:\r<BR>\n" );
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document.write( "1.00 ( g + s )\r<BR>\n" );
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document.write( "Now set the two expressions for the price of the mixture equal to each other and solve for \"g\":\r<BR>\n" );
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document.write( "1.50 g + 0.40 s = 1.00 ( g + s )<BR>\n" );
document.write( "1.50 g + 0.40 s = 1.00 g + 1.00 s<BR>\n" );
document.write( "1.50 g - 1.00 g = 1.00 s - 0.40 s<BR>\n" );
document.write( "0.50 g = 0.60 s<BR>\n" );
document.write( "g = (0.60 / 0.50) s<BR>\n" );
document.write( "g = 1.2 s\r<BR>\n" );
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document.write( "From this we see that we need 1.2 gallons of gas for every gallon of substitute fuel.\r<BR>\n" );
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document.write( "We can now calculate the percentage of substitute fuel in the mixture:\r<BR>\n" );
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document.write( "s / (g + s) = s / (1.2s + s) = s / 2.2s = 0.4545, or 45.45%\r<BR>\n" );
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document.write( "To check our solution, verify that 45.45% of the substitute fuel price added to 100 - 45.45 = 54.55% of the gas price equals $1.00:\r<BR>\n" );
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document.write( "0.5455($1.50) +  0.4545($0.40) = $1.00\r<BR>\n" );
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document.write( "It does! </SPAN>\n" );
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