SOLUTION: when carrying 18 gallons of fuel, the airplane weighs 2117 pounds. when carrying 44 gallons of fuel, it weighs 2286 pounds. how much does the airplane weigh if it is carrying 48 ga

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: when carrying 18 gallons of fuel, the airplane weighs 2117 pounds. when carrying 44 gallons of fuel, it weighs 2286 pounds. how much does the airplane weigh if it is carrying 48 ga      Log On


   

Question 1104050: when carrying 18 gallons of fuel, the airplane weighs 2117 pounds. when carrying 44 gallons of fuel, it weighs 2286 pounds. how much does the airplane weigh if it is carrying 48 gallons of fuel?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
(x,y) for (Gallons of Fuel, Weight of Plane)

(18,2117)
(44,2286)
(48, v)

Various ways to find v, all very much related. Just find the line between the first two given points.

y-2117=%28%282286-2117%29%2F%2844-18%29%29%28x-18%29
y-2117=%28169%2F26%29%28x-18%29
y-2117=%286.5%29%28x-18%29
y-2117=6.5x-117
highlight_green%28y=6.5x%2B2000%29------showing that the plane without fuel is 2000 pounds.

Now v=y=6.5%2A48%2B2000
highlight%28v=2312%29---------when plane has 48 gallons of fuel

Answer by ikleyn(52797) About Me  (Show Source):
You can put this solution on YOUR website!
.
It follows directly from the condition that 44-18 = 26 gallons of fuel weight 2286-2117 = 169 pounds.


Hence, 1 gallon of fuel weights 169%2F26 = 6.5 pounds.


Then 4 = 48-44 gallons weight 4*6.5 = 26 pounds,  


and the answer to the problem's question is 2286 + 26 = 2312 pounds.


All these calculations you can perform MENTALLY, so this problem is for MENTAL solution.

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    - Solving mentally word problems on two equations in two unknowns
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