Question

Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 12 gallons of fuel, the airplane weighs 2078 pounds. When carrying 40 gallons of fuel, it weighs 2260 pounds. How much does the airplane weigh if it is carrying 54 gallons of fuel?

Answer 1

To find the weight of the airplane when carrying 54 gallons of fuel, you can use the given data to create a linear equation and solve it. The weight of the airplane is approximately 2311 pounds when carrying 54 gallons of fuel.

Step-by-step explanation:

To find the weight of the airplane when carrying 54 gallons of fuel, we can use the information given to create a linear equation. Let's denote the weight of the airplane as W and the amount of fuel in gallons as F. We can write two equations using the given data:

When carrying 12 gallons of fuel, the airplane weighs 2078 pounds: W = 2078

When carrying 40 gallons of fuel, the airplane weighs 2260 pounds: W = 2260

We can solve this system of equations to find the slope and y-intercept of the linear function. Subtracting the second equation from the first equation, we get 182 = 1820 - 40F. Solving for F, we find F = 5. Substituting this value back into any of the equations, we find W = 2078 + (2018/7) = 2310.57 pounds. Therefore, the airplane weighs approximately 2311 pounds when carrying 54 gallons of fuel.

Answer 2

`2351\text{ pounds}`

Step-by-step explanation:

GIVEN: Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying
`12` gallons of fuel, the airplane weighs
`2078` pounds. When carrying
`40` gallons of fuel, it weighs
`2260` pounds.

TO FIND: How much does the airplane weigh if it is carrying
`54` gallons of fuel.

SOLUTION:

Let the fuel be represented along
`\text{x-axis}` and weight of plane along
`\text{y-axis}`

two coordinates are
`(12,2078)\text{ and }(40,2260)`

now, equation of linear function is

`\text{y}-\text{y}_1=\frac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}(\text{x}-\text{x}_1)`

putting values we get

`\text{y}-2078=(182)/(28)(\text{x}-12)`

`2\text{y}=13\text{x}+4000`

Now when fuel is
`54\text{ gallons}`

`2\text{y}=13*54+4000`

`\text{y}=2351\text{ pounds}`

Airplane weighs
`2351\text{ pounds}`