Pls help!!!!!!! its applications in pre calc

Mathematics

1 answer:

andreev551 [17]2 years ago

8 0

The total weight W of such a plane is equal to

W = w + gf

where

w = weight of plane without fuel

g = number of gallons of fuel

f = weight of 1 gallon of fuel.

When carrying g = 10 gallons, the total weight is W = 1955, so

1955 = w + 10f

When carrying g = 42 gallons, the weight is W = 2131, so

2131 = w + 42f

We want to find W when g = 52, and to do this we first need to find the weight of the plane w and the weight of 1 gallon of fuel f.

Solve the system of equations,

w + 10f = 1955

w + 42f = 2131

We can combine the equations like so to eliminate w and solve for f :

(w + 42f) - (w + 10f) = 2131 - 1955

32f = 176

f = 11/2 = 5.5

Then solving for w, we get

w + 10 (5.5) = 1955

w + 55 = 1955

w = 1900

So, when the plane carries g = 52 gallons of fuel, the total weight is

W = 1900 + 52 (5.5) = 2186

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