how many acres of each should Jan plant if she wants the same amount of corn and soybeans?

Question

Jan has 150 acres of farm land that she wants to plant with either corn or soybeans. If 200 bushels of corn grow per acre and 800 bushels of soybeans grow per acre, how many acres of each should Jan plant if she wants the same amount of corn and soybeans?

Answer 1

I always start out these types of problems by defining our variables.

Let x = acres of corn

y = acres of soybeans

You know that you have 150 acres total so:

x + y = 150

They give you the info that you get 200 bushels of corn per acre and 800 bushels of soybeans per acre but you want to harvest the same amount of soybeans and corn. You can use the following equation to represent this

200x = 800y

You now have to solve your system of equations

200x = 800y

x + y = 150

I decided to solve the first one for x

200x = 800y (divide by 200)

x = 4y

Substitute into the other equation x + y = 150

(4y) + y = 150 (add the 4y + y)

5y = 150 (divide by 5)

y = 30

Substitute into any previous equation with both x and y

x = 4y

x = 4(30) = 120

You have to plant 120 acres of corn and 30 acres of soybeans.

Please let me know if you have any questions! I used to be a finite math instructor, so I love tutoring this class.