Question 68320: An oil company wants to mix two grades of rocket fuel costing $3 and $4 per gallon,respectively with purified ethanol costing $8 per gallon to obtain 140 gallons of hybrid fuel costing NASA $6 per gallon. If the oil company also wants the amount of lower grade fuel to be twice that of higher-grade rocket fuel,how many gallons of each variety of fueling product should be mixed?
- define your unknowns in terms of x,y etc.
-write down a linear function of equations representing the information given
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! An oil company wants to mix two grades of rocket fuel costing $3 and $4 per gallon,respectively with purified ethanol costing $8 per gallon to obtain 140 gallons of hybrid fuel costing NASA $6 per gallon. If the oil company also wants the amount of lower grade fuel to be twice that of higher-grade rocket fuel,how many gallons of each variety of fueling product should be mixed?
- define your unknowns in terms of x,y etc.
-write down a linear function of equations representing the information given
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Let amount of $3 fuel be x ; value is 3x dollars
Let amount of $4 fuel be 2x; value is 4(2x)=8x dollars
Let amount of ethanol fuel be 140-3x: value = 8(140-3x)=1120-24x dollars
Amount of mixture = 140 gallons: value = 6*140=840
EQUATIOn:
value+value+value= 840 dollars
2x+8x+1120-24x=840
-14x=--280
x=20 gals (amount of $3 fuel in mixture)
2x=40 gals (amount of $4 fuel in mixture)
140-60=80 gals (amount of $8 ethanol in the mixture)
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Cheers,
Stan H.
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