SOLUTION: 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 mixtu

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Question 708854: 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?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
"What percent of the mixture", means for 100 parts. First set up the cost equation.

x and y, the gallons or just parts of each fuel to mix. x the fuel, y the substitute.

2.48x%2B1.82y=2.15 dollars (so this uses x and y as gallons). That is for 1 gallon of mixture.

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.

We just have this system:
2.48x%2B1.82y=2.15
x%2By=1

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).
2.48x-1.82x+1.82y-1.82y=2.15-1.82(1)
0.66x=0.33
highlight%28x=0.5%29
That means y is also highlight%280.5%29

ANSWER: Half gallon for each one to make 1 gallon of fuel mixture at 2.15 dollars per gallon. 50% of each fuel.