Question

A farmer fills his field proportionately with soybeans and corn. Last year he planted 200 acres of corn and 50 acres of soybeans. Answer these questions in the textbox or upload your work.

a) Are the number of acres of corn and the number of acres of soybeans directly proportional or inversely proportional? Explain your answer.

b) What is the constant of proportionality? Tell how you found it.

c) Let x equal the number of acres of corn and y equal the number of acres of soybeans. Write an equation to show this relationship.

d) How many acres of soybeans can the farmer plant this year if he plants 250 acres of corn? Show your work.

Answer 1

Answer:

Part A)  Is a directly proportional

Part B) The constant of proportionality is $k=0.25$

Part C) The equation is $y=0.25x$

Part D) $62.5$  acres of soybeans

Step-by-step explanation:

Part A) Are the number of acres of corn and the number of acres of soybeans directly proportional or inversely proportional?

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$

Let

x-----> the number of acres of corn

y---->  the number of acres of soybeans

so

$y/x=k$  

if the number of acres of corn increases then the number of acres of soybeans increases

if the number of acres of corn decreases then the number of acres of soybeans decreases

therefore

The relationship is a directly proportional

Part B) What is the constant of proportionality?

we have that

For x=200, y=50

substitute

$y/x=k$

$k=50/200$

$k=0.25$

Part C) Let x equal the number of acres of corn and y equal the number of acres of soybeans. Write an equation to show this relationship.

The linear equation that represent the direct variation is equal to

$y/x=k$

we have

$k=0.25$

substitute

$y/x=0.25$

$y=0.25x$

Part D) How many acres of soybeans can the farmer plant this year if he plants 250 acres of corn?

For x=250

Find the value of y

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

$y=0.25(250)=62.5$ -----> acres of soybeans