Suppose that the weight (in pounds) of an airplane is a linear function of the total amount of fuel (in gallons) 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 6.4. With 54 gallons of fuel in its tank, the airplane has a weight of 2245.6 pounds. What is the weight of the plane with 82 gallons of fuel in its tank?

Answer 1

A linear equation takes the form of

y=mx+b....Eq1 (Slope-Intercept Form)

 

Where.....

x=#gallons of fuel

y=total weight of plane including fuel

m=slope=6.4......................given in prob statement

b=weight of plane, no fuel....a constant to be calc'd

 

Substitute these values into the equation Eq1....

          y=mx+b

2245.6=6.4(54)+b.........solve for "b"

2245.6=345.6+b

     ∴ b=1900................weight of plane, no fuel

 

Now substitute "b=1900" into the Eq1......

        y=6.4x+1900........Eq2 used to calc total weight

                                     any amount of gallons fuel used

 

Question asks for total weight with 82 gallons of fuel.  

Substitute x=82 into Eq2 and solve for"y".

    y=6.4x+1900..........Eq2

    y=6.4(82)+1900

    y=524.8+1900

∴ y=2424.8 

 

So total plane weight with 82gallons fuel is 2424.80 lbs.

 

 

 

 

Answer 2

First we need to find the constant B and then use that to find the weight of the air plan when X = 82

 

Y = 6.4 (82) + 1900

 

= 2424.8 is the weight of the air craft