Answer: 2561.7 pounds
Explanation:
If we assume the total weight of an airplane (in pounds units) as a linear function of the amount of fuel in its tank (in gallons) and we make a Weight vs amount of fuel graph, which resulting slope is 5.7, we can use the slope equation of the line:
[tex]m=\frac{Y-Y_{1}}{X-X_{1}}[/tex] (1)
Where:
[tex]m=5.7[/tex] is the slope of the line
[tex]Y_{1}=2390.7pounds[/tex] is the airplane weight with 51 gallons of fuel in its tank (assuming we chose the Y axis for the airplane weight in the graph)
[tex]X_{1}=51gallons[/tex] is the fuel in airplane's tank for a total weigth of 2390.7 pounds (assuming we chose the X axis for the a,ount of fuel in the tank in the graph)
This means we already have one point of the graph, which coordinate is:
[tex](X_{1},Y_{1})=(51,2390.7)[/tex]
Rewritting (1):
[tex]Y=m(X-X_{1})+Y_{1}[/tex] (2)
As Y is a function of X:
[tex]Y=f_{(X)}=m(X-X_{1})+Y_{1}[/tex] (3)
Substituting the known values:
[tex]f_{(X)}=5.7(X-51)+2390.7[/tex] (4)
[tex]f_{(X)}=5.7X-290.7+2390.7[/tex] (5)
[tex]f_{(X)}=5.7X+2100[/tex] (6)
Now, evaluating this function when X=81 (talking about the 81 gallons of fuel in the tank):
[tex]f_{(81)}=5.7(81)+2100[/tex] (7)
[tex]f_{(81)}=2561.7[/tex] (8) This means the weight of the plane when it has 81 gallons of fuel in its tank is 2561.7 pounds.
