Question

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 14 gallons of fuel, the airplane eeighs 2191 pounds. When carrying 40 gallons of fuel, it weigh 2360 pounds. How much does the airplane weigh if it is carrying 56 gallons of fuel?

Answer 1

The answer is: 2464

So you first set the equations with the information provided

14(weight of 1 gallon) + x = 2191

40(weight of 1 gallon) + x = 2360

So we now solve for x, substracting the first equation from the second one we get that

26(weight of 1 gallon) = 196

this implies that weight of 1 gallon is 196/26= 6.5

Now we susbtitute in the first equation and get that

x=2191 - 46(6.5)=2100

where x is the weight of the airplane

Finally, we add 2100 + 56(weight of 1 gallon) = 2100 +56(6.5) = 2464