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 15 gallons of fuel, the airplane weighs 2087 pounds. When carrying 40 gallons of fuel, it weighs 2232 pounds. How much does the airplane weigh if it is carrying 50 gallons of fuel?

Step 1 ：Let's denote the weight of the airplane as \(y\) and the amount of fuel as \(x\). The relationship between \(y\) and \(x\) is a linear function, which can be represented by the equation \(y = mx + c\), where \(m\) is the slope of the line and \(c\) is the y-intercept.

Step 2 ：We can find the slope \(m\) by calculating the change in weight divided by the change in the amount of fuel. Given that the airplane weighs 2087 pounds when carrying 15 gallons of fuel and 2232 pounds when carrying 40 gallons of fuel, the slope \(m\) is \((2232 - 2087) / (40 - 15) = 5.8\).

Step 3 ：We can find the y-intercept \(c\) by substituting the values of a point \((x, y)\) and the slope \(m\) into the equation of the line. Using the point \((15, 2087)\), we get \(c = 2087 - 5.8 \times 15 = 2000.0\).

Step 4 ：Now that we have the equation of the line \(y = 5.8x + 2000.0\), we can find the weight of the airplane when it is carrying 50 gallons of fuel by substituting \(x = 50\) into the equation. This gives us \(y = 5.8 \times 50 + 2000.0 = 2290.0\).

Step 5 ：Final Answer: The airplane weighs \(\boxed{2290}\) pounds when it is carrying 50 gallons of fuel.