Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in ga

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    math_celebrity Administrator Staff Member

    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 2012 pounds. When carrying 55 gallons of fuel, it weighs 2208 pounds. How much does the airplane weigh if it is carrying 65 gallons of fuel?

    Linear functions are written in the form of one dependent variable and one independent variable. Using g as the number of gallons and W(g) as the weight, we have:
    W(g) = gx + c where c is a constant

    We are given:
    • W(20) = 2012
    • W(55) = 2208
    We want to know W(65)

    Using our givens, we have:
    W(20) = 20x + c = 2012
    W(55) = 55x + c = 2208

    Rearranging both equations, we have:
    c = 2012 - 20x
    c = 2208 - 55x

    Set them both equal to each other:
    2012 - 20x = 2208 - 55x

    Add 55x to each side:
    35x + 2012 = 2208

    Using our equation solver, we see that x is 5.6

    Plugging x = 5.6 back into the first equation, we get:
    c = 2012 - 20(5.6)
    c = 2012 - 112
    c = 2900

    Now that we have all our pieces, find W(65)
    W(65) = 65(5.6) + 2900
    W(65) = 264 + 2900
    W(65) = 3264


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