SOLUTION: Suppose that the weight of a plane is a linear function of the amount of fuel in its tank. When carrying 15 gallons of fuel, the airplane weighs 1987 pounds. When carrying 40 gallo

Algebra ->  Linear-equations -> SOLUTION: Suppose that the weight of a plane is a linear function of the amount of fuel in its tank. When carrying 15 gallons of fuel, the airplane weighs 1987 pounds. When carrying 40 gallo      Log On


   

Question 1144178: Suppose that the weight of a plane is a linear function of the amount of fuel in its tank. When carrying 15 gallons of fuel, the airplane weighs 1987 pounds. When carrying 40 gallons of fuel, it weighs 2132 pounds. How much does the airplane weight if it is carrying 50 gallons of fuel ?
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

Airplane + 40 gallons of fuel weights 2132 pounds.   (1)

Airplane + 15 gallons of fuel weights 1987 pounds.   (2)
----------------------------------------------------------Subtract (2) from (1). You will get

           25 gallons of fuel weight 2132 - 1987 = 145 pounds.  ====>

====>       1 gallon of fuel weights 145%2F25 = 29%2F5 = 5.8 pounds.


(Airplane + 50 gallons of fuel)'s weight = (Airplane + 40 gallons of fuel weight) +  (10 gallons of fuel weight) = 

                                            2132 + 10*5.8 = 2132 + 58 = 2190 pounds.


Answer.  Airplane with 50 gallons of fuel weights 2190 pounds.

----------------

Compare it with the problem 5 of the lesson
    - Solving mentally word problems on two equations in two unknowns
in this site.

Same problem, different numbers.

And the same idea / methodology of the solution.


Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
--------------------
..., weight of a plane is a linear function of the amount of fuel in its tank. When carrying 15 gallons of fuel, the airplane weighs 1987 pounds. When carrying 40 gallons of fuel, it weighs 2132 pounds.
---------------------------


Two points of a line, (15,1987) & (40,2132).
(x,y) points

y-2132=%28%282132-1987%29%2F%2840-15%29%29%28x-40%29, using point-slope form;

y=%285%264%2F5%29%28x-40%29%2B2132
y=5.8x-232%2B2132
highlight_green%28y=5.8x%2B1900%29

--------------------------
How much does the airplane weight if it is carrying 50 gallons of fuel ?
--------------------------

Let x equal 50, and evaluate y.