Old McDonald has 500 acres of land to plant in corn and soybeans. The cost of cultivating corn is $42 per acre and the cost of cultivating soybeans is $30 per acre. Old McDonald has $18,600 available for cultivating these crops. If Old McDonald wishes to use all the allotted acres and his entire budget for cultivating corn and soybeans, how many acres of each crop should he plant? Define variable(s). Set up equations.
This is what I did:
X= corn
Y= Soybeans
My unknown must be the number of acres.
I set it up like this:
x+y = 500
42x+30y=18,600
x/corn= 300 and y/soybeans=200
Be more precise in your definitions of the variables.
Let x be the number of acres of corn
Let y be the number of acres of soybeans
Your two equations are correct, but how did you solve them?
Your final statement of
"x/corn= 300 and y/soybeans=200" makes no sense to me.
x+y=500 ---> y=500-x
42x+30(500-x)=18,600
42x+15000-30x=18,600
12x+15000-15000=18600-15000
12x=3600
x=300
300+y=500
300-300+y=500-300
y=200
Good job on setting up the equations!
To find the number of acres of each crop that Old McDonald should plant, we can use a system of equations to represent the given information.
Let's break it down:
First, we define the variables:
Let X represent the number of acres planted in corn.
Let Y represent the number of acres planted in soybeans.
Now, let's set up the equations:
1. Equation representing the total number of acres:
Since Old McDonald wants to use all 500 acres of land, the equation is:
X + Y = 500
2. Equation representing the total cost:
The cost of cultivating corn is $42 per acre, and the cost of cultivating soybeans is $30 per acre. Since Old McDonald wants to use his entire budget of $18,600, the equation is:
42X + 30Y = 18,600
So, the two equations that represent the given information are:
X + Y = 500
42X + 30Y = 18,600
Now, you can solve this system of equations to find the values of X and Y, which will represent the number of acres of corn and soybeans that Old McDonald should plant.