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.Com
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(39620)   (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.





------showing that the plane without fuel is 2000 pounds.

Now
---------when plane has 48 gallons of fuel
Answer by ikleyn(52798)   (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  = 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.

------------
See the lesson
    - Solving mentally word problems on two equations in two unknowns
in this site.


RELATED QUESTIONS

Suppose that the weight (in pounds) of an airplane is a linear function of the amount of... (answered by ikleyn)
suppose that the weight in pounds of an airplane is a linear function of the amount of... (answered by josgarithmetic)
Suppose that the weight (in pounds) of an airplane is a linear function of the amount of... (answered by josgarithmetic,ikleyn)
Suppose that the weight (in pounds) of an airplane is a linear function of the amount of... (answered by Shin123)
Suppose that the weight (in pounds) of an airplane is a linear function of the amount of... (answered by stanbon)
Suppose that the weight (in pounds) of an airplane is a linear function of the amount of... (answered by Alan3354)
Suppose that the weight (in pounds) of an airplane is a linear function of the amount of... (answered by ikleyn)
Suppose that the weight (in pounds) of an airplane is a linear function of the amount of... (answered by Alan3354)
Suppose that the weight (in pounds) of an airplane is a linear function of the amount of... (answered by ikleyn,josgarithmetic)