SOLUTION: Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 18 gallons of fuel, the airplane weighs 1999 p

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Question 1102168: Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 18 gallons of fuel, the airplane weighs 1999 pounds. When carrying 50 gallons of fuel, it weighs
2175 pounds. How much does the airplane weigh if it is carrying 60 gallons of fuel?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The description illustrates two linear points, (18,1999) and (50,2175). The two points are to fit on a line.

The line's equation can be found function formed, and the value evaluated for 60 gallons of fuel;
OR
Extrapolation can be used.

.
FUEL        WEIGHT
18           1999
50           2175
60            ?


%2860-50%29%2Fd=%2850-18%29%2F%282175-1999%29
d%2F10=176%2F32
d=1760%2F32
d=55
Weight for 60 gallons: 2175%2B55=highlight%282230%29 pounds.



-
If solve using linear equation
known point (50,2175)
y-2175=%28%282175-1999%29%2F%2850-18%29%29%28x-50%29, point-slope-form
highlight_green%28y=5.5x%2B1900%29
Let x=60, find y=2230

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Airplane + 50 gallons of fuel weights 2175 pounds.   (1)

Airplane + 18 gallons of fuel weights 1999 pounds.   (2)
----------------------------------------------------------Subtract (2) from (1). You will get

           32 gallons of fuel weight 2175 - 1999 = 180 pounds.  ====>

====>       1 gallon of fuel weights 180%2F32 = 5.625 pounds.


(Airplane + 60 gallons of fuel)'s weight = (Airplane + 50 gallons of fuel weight) + weight of 10 gallons of fuel = 

                                            2175 + 10*5.625 =  2231.25 pounds.


Answer.  Airplane with 60 gallons of fuel weights 2231.25 pounds.