Linear functions

Question

Suppose that the weigh(in pounds) of an airplane is a linear function of the amount of fuel( in gallons) in its tank. When carrying 20 gallons of fuel, the airplane weighs 2030 pounds. When carrying 48 gallons of fuel, it weighs 2212 pounds. How much does the airplane weigh if it is carrying 52 gallons of fuel?

Answer 1

2030= 20+2010 with 20 lbs of fuel

2212 = 202 + 2010 with 48 lbs of fuel

the additional 28 lbs added 182 lbs or 182/28 per lb over 20 lb = 91/14 = 6.5 per lb

2010 + 202 + (91/14)(4) = 2212+ 182/7= 2212+ 26= 2238 lbs with 52 lbs of fuel

total weight = 2030 + (91/14)(f-20)

or

TW(f) = 1900+6.5f

TW(20) = 1900+6.5(20) = 1900+130=2030

TW(48) = 1900+6.5(48) =1900+312= 2212

TW(52) = 1900+6.5(52) =1900+338= 2238

with zero fuel, the plane weighs 2030-(13/2)(20) = 1900 lbs = plane weight alone

for some reason the fuel weight increases the total weight by 6 1/2 times the fuel weight. maybe due to container costs or extra staff on the plane?