Respuesta :
Let 'y' be the weight of the airplane corresponding to when the amount of fuel is 'x'.
Given that the airplane weighs 2104 when fuel is 16 gallons, this can be represented as the ordered pair,
[tex](16,2104)[/tex]Also, given that the airplane weighs 2312 when fuel is 48 gallons.The corresponding ordered pair will be,
[tex](48,2312)[/tex]It is mentioned that there is a linear relationship between the amount of fuel (x), and the weight of airplane (y).
Consider that the equation of a straight line passing through two given points is given by,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}\cdot(x_2-x_1)[/tex]As per the given problem,
[tex]\begin{gathered} (x_1,y_1)=(16,2104) \\ (x_2,y_2)=(48,2312) \end{gathered}[/tex]Substitute the values,
[tex]\begin{gathered} y-2104_{}=\frac{2312-2104}{48-16}\cdot(x-16) \\ y-2104_{}=\frac{13}{2}\cdot(x-16) \\ y-2104=\frac{13}{2}x-104 \\ y=\frac{13}{2}x-104+2104 \\ y=\frac{13}{2}x+2000 \end{gathered}[/tex]At the instant when the fuel is 66 gallons,
[tex]x=66[/tex]The corresponding weight of airplane is calculated as,
[tex]\begin{gathered} y=\frac{13}{2}(66)+2000 \\ y=429+2000 \\ y=2429 \end{gathered}[/tex]Thus, the airplane weighs 2429 if it is carrying 66 gallons of fuel.
