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 10 gallons of fuel, the airplane weighs 2055

Algebra ->  Linear-equations -> 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 10 gallons of fuel, the airplane weighs 2055       Log On


   

Question 1197369: 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 10 gallons of fuel, the airplane weighs 2055 pounds. When carrying 42 gallons of fuel, it weighs 2231 pounds. How much does the airplane weigh if it is carrying 46 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!
y-k=m(x-h)
points (10,2055) and (42,2231)
or you could simply use linear interpolation for this unknown point (46, w).

Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
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 10 gallons of fuel, the airplane weighs 2055 pounds.
When carrying 42 gallons of fuel, it weighs 2231 pounds.
How much does the airplane weigh if it is carrying 46 gallons of fuel?
~~~~~~~~~~~~~~~~~~~


            It is a standard entertainment problem to solve it  MENTALLY  without using equations. 


Airplane + 10 gallons of fuel weights 2055 pounds.   (1)

Airplane + 42 gallons of fuel weights 2231 pounds.   (2)
----------------------------------------------------------Subtract (2) from (1). You will get

           32 gallons of fuel weight 2231 - 2055 = 176 pounds.  ====>

====>       1 gallon of fuel weights 176%2F32 = 5.5 pounds.


(Airplane + 46 gallons of fuel)'s weight = (Airplane + 42 gallons of fuel weight) + weight of 4 gallons of fuel = 

                                         =  2231 + 4*5.5 =  2253 pounds.


Answer.  Airplane with 46 gallons of fuel weights 2253 pounds.

Solved.