The total operating cost to run the organic strawberry farm varies directly with its number of acres. What is the constant of variation in this scenario? If the total operating cost for a 20-acre organic strawberry farm is $551,520, how many acres are on a farm with a total operating cost of $441,216? acres

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Let

x ----> the number of acres

y ---> total operating costs

we have the ordered pair (20,551,520)

For x=20 acres, y=$551,520

Find the value of the constant of proportionality k

[tex]k=\frac{y}{x}[/tex]

substitute the values of x and y

[tex]k=\frac{551,520}{20}=\$27,576\ per\ acre[/tex]

The linear equation is equal to

[tex]y=27,576x[/tex]

Find out how many acres are on a farm with a total operating cost of $441,216

so

For y=$441,216

substitute in the linear equation the value of y and solve for x

[tex]441,216=27,576x[/tex]

[tex]x=441,216/27,576[/tex]

[tex]x=16\ acres[/tex]

Eduard22sly Eduard22sly · Answer 2 · 2022-04-25T17:26:17+02:00

Given the data from the question, the answers to the questions given are illustrated below:

A. How to determine the constant

Let the total cost be C
Let the number of acres be A

From the question given above,

C ∝ A

C = KA

K = C / A

Total cost (C) = $ 551520
Number of acres (A) = 20 acres
Conctant (K) =?

K = C / A

K = 551520 / 20

K = 27576 dollar/acre

B. How to determine the number of acres

Total cost (C) = $ 441216
Constant (K) = 27576 dollar/acre
Number of acres (A) =?

C = KA

Divide both side by K

A = C / K

A = 441216 / 27576

A = 16 acres

Learn more about variation:

https://brainly.com/question/14254277