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 20 gallons of fuel, the airplane weighs 2030 pounds. When carrying 54 gallons of fuel, it weighs 2251 pounds. How much does the airplane weigh if it is carrying 64 gallons of fuel?

Answer 1

Answer:

2316 pounds

Step-by-step explanation:

If this is linear, we can create 2 coordinate points for the gallons of fuel and weight of the plane.  If the plane weighs 2030 pounds with 20 gallons of fuel, the coordinate point is (20, 2030).  If the plane weights 2251 with 54 gallons of fuel, the coordinate point is (54, 2251).  We can use those 2 points to find the slope of the line:

$m=\frac{2251-2030}{54-20}=6.5$

This means that for every gallon of gas, the plane's weight increases by 6.5 pounds.  Now that we have the slope, we can plug that in, along with one of the points we created, to find the model for this situation.  Use the point-slope form:

y - 2030 = 6.5(x - 20) and

y - 2030 = 6.5x - 130 so

y = 6.5x + 1900

This means that if there was NO gas at all in the plane, x = 0, the plane weighs 1900 pounds.  Now we can use that model to find the weight of the plane, y, when x = 64 gallons:

y = 6.5(64) + 1900 so

y = 2316 pounds.