Suppose that the weight in pounds of an airplane is a linear

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 25 gallons of fuel, the airplane weighs 2045 pounds. When carrying 40 gallons of fuel, it weighs 2132 pounds. How much does the airplane weigh if it is carrying 50 gallons of fuel?

Solution

Let the weight (in pounds) of the airplane be ax +b , where x is the amount of fuel (in gallons), and a,b, are arbitrary real numbers. When carrying 25 gallons of fuel, the airplane weighs 2045 pounds so that a*25 +b = 2045 or, 25a +b = 2045…(1). Also, when carrying 40 gallons of fuel, the airplane weighs 2132 pounds. so that a*40 +b = 2132 or, 40a+b = 2132…(2). Now, on subtracting the 1^st equation from the 2^nd equation, we get 40a+b -25a-b = 2132-2045 or, 15a = 87 so that a = 87/15 = 29/5. Now, on substituting a = 29/5 in the 1^st equation, we get 25*29/5+b = 2045 or, 145 +b = 2045 so that b = 2045-145 = 1900. Then, the weight (in pounds) of the airplane is (29/5)x +1900, where x is the amount of fuel (in gallons). Therefore, when carrying 50 gallons of fuel, the airplane will weigh (29/5)*50+1900 = 290+1900 = 2190 pounds.