What is the weight of the plane with 77 gallons of fuel in its tank?

Question

Suppose that the weight (in pounds) of an airplane is a linear function of the total amount of fuel (in gallons) in its tank. When graphed, the function gives a line with a slope of
6.5
. See the figure below.
With
47
gallons of fuel in its tank, the airplane has a weight of
2305.5
pounds. What is the weight of the plane with
77
gallons of fuel in its tank?

Answer 1

Let's find a general equation satisfying the prob statement 

parameters in point-intercept form (y=mx+b)...

 

Let....

y=plane total weight with fuel,

x=gallons of fuel,

b=weight of plane, empty (no fuel)

 

We are given the slope of the linear equation, so it reads...

y=6.5x+b

 

We are given the plane weight 2305.5 lbs (y) when 47gal of

fuel (x) are used.  These values can be rewritten as an ordered

coordinate pair (x,y)=(47, 2305.5).  Let's plug those values

into our equation and solve for "b."

 

2305.5=6.5(47)+b

2305.5=305.5+b.........simplify

     ∴ b=2000..............subtract 305.5 from both sides

 

So our general equation reads...

   y=6.5x+2000...........Eq1

 

Now plug in the problem value for "x=77" into our Eq1

and solve for "y"..........

    y=6.5(77)+2000.....substitute 77 for "x"

    y=500.5+2000........simplify

∴ y=2500.5................subtract 500.5 from both sides

 

So the total plane weight with 77gal of fuel is 2500.5lbs, 

represented by the coordinate ordered pair (77, 2500.5).

 

We can use our general equation to calculate for any other

combination of values (x,y) for "x=total plane weight, y=gallons

of fuel."