SOLUTION: A pilot has a Cessna 172 Skyhawk airplane with a fuel tank that holds 56 gallons of 100LL fuel. The pilot charges his passenger $4.00 per gallon for the amount of old fuel that is

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Question 1157494: A pilot has a Cessna 172 Skyhawk airplane with a fuel tank that holds 56 gallons of 100LL fuel. The pilot charges his passenger $4.00 per gallon for the amount of old fuel that is already in the tank. The pilot then fills the rest of the tank with new fuel that costs $7.36 per gallon. The pilot bills the passenger $328.16 for the combined cost of the old fuel and new fuel. How many gallons of new fuel were required to fill the tank?
Answer by mathslover(157) About Me  (Show Source):
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Let the quantity of old fuel be x
Quantity of new fuel be y
since total capacity of the tank is 56
=> x + y = 56 ..... (1)
Also , total cost of fuel
= 4x + 7.36y = 328.16 ....(2)
Multiplying equation (1) with 4 we get,
4x + 4y = 224 --------- (3)
Subtracting equation 3 from equation 2 we get,
3.36 y = 104.16
therefore y= 104.16/3.36 = 31
therefore new fuel is 31 gallon.
Old fuel = 56 - 31 = 25 gallon
Ans: 31 gallons of new fuel were required to fill the tank.