document.write( "Question 478492: As one alternative to gasoline-powered vehicles, flex fuel vehicles can use both regular gasoline and E85, a fuel containing 85% ethanol. The ethanol in E85 is derived from corn and other plants, a renewable resource, and burning E85 results in less pollution than gasoline. Because using E85 results in a lower fuel economy, its price per gallon must be lower than the price of gasoline in order to make it an economical fuel option. A 2007 Chevrolet Tahoe gets 21 mpg on the highway using gasoline and only 15 mpg on the highway using E85. If the price of gasoline is $3.36 a gallon, what must the price of E85 be in order for the fuel cost per mile to be the same? \n" ); document.write( "
Algebra.Com's Answer #327842 by Theo(13342)\"\" \"About 
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tahoe gets 21 mpg with gasoline and 15 mpg with ethanol.
\n" ); document.write( "cost for gas is $3.36.
\n" ); document.write( "cost for ethanol is x.
\n" ); document.write( "you want to know what the cost of ethanol should be to make gas and ethanol financially equivalent.
\n" ); document.write( "the formula that will help you find the equivalence is:
\n" ); document.write( "cpm = cpg / mpg
\n" ); document.write( "cpm = cost per mile
\n" ); document.write( "cpg = cost per gallon
\n" ); document.write( "mpg = miles per gallon
\n" ); document.write( "for gasoline, this formula would result in:
\n" ); document.write( "cpm = 3.36 / 21 = .16
\n" ); document.write( "for ethanol, this formula would result in:
\n" ); document.write( "cpm = cpg / 15
\n" ); document.write( "to get equivalence, you need to replace cpm with what we derived for gasoline.
\n" ); document.write( "the equation becomes:
\n" ); document.write( ".16 = cpg / 15
\n" ); document.write( "multiply both sides of this equation by 15 to get:
\n" ); document.write( "cpg = .16 * 15 which equals 2.4
\n" ); document.write( "the cost of ethanol per gallon needs to be 2.4 in order to make it financially equivalent to gasoline.
\n" ); document.write( "go back to your original equations:
\n" ); document.write( "for gasoline:
\n" ); document.write( "cpm = cpg / mpg = 3.36 / 21 = .16
\n" ); document.write( "for ethanol:
\n" ); document.write( "cpm = cpg / mpg = 2.4 / 15 = .16
\n" ); document.write( "gas and ethanol are comparable when the cost of ethanol is equal to $2.40 per gallon.
\n" ); document.write( "the formula was derived as follows:
\n" ); document.write( "m = number of miles
\n" ); document.write( "c = cost
\n" ); document.write( "mpg = miles per gallon
\n" ); document.write( "cpg = cost per gallon
\n" ); document.write( "m = g * mpg
\n" ); document.write( "this says that the number of miles you can travel is equal to the number of gallons you have * the miles per gallon.
\n" ); document.write( "c = g * cpg
\n" ); document.write( "this says that the total cost is equal to the number of gallons you bought times the cost per gallon.
\n" ); document.write( "if you want to get cost per mile (cpm) then you have to divide c by m to get:
\n" ); document.write( "cpm = c/m
\n" ); document.write( "since c = g*cpg and since m = g*mpg, you can substitute for c/m to get:
\n" ); document.write( "cpm = (g*cpg)/(g*mpg)
\n" ); document.write( "the g in the numerator and denominator cancels out and you are left with:
\n" ); document.write( "cpm = cpg/mpg
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