Question

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

Answer 1

Answer:

$16\ acres$

Step-by-step explanation:

we know that

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

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

$k=\frac{y}{x}$

substitute the values of x and y

$k=\frac{551,520}{20}=\ 27,576\ per\ acre$

The linear equation is equal to

$y=27,576x$

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

$441,216=27,576x$

$x=441,216/27,576$

$x=16\ acres$

Answer 2

Answer:

Step-by-step explanation:

16 acres