A farmer plans to plant 270 acres of his farm with wheat and soybeans. For every 2 acres of land planted with soybeans, the farmer wants to plant 7 acres of land with wheat. The farmer uses the following system of equations to determine how many acres of each crop he should plant.
w + s = 270
7s - 2w = 0
w is the number of acres planted with wheat, and s is the number of acres planted with soybeans.
How many acres should the farmer plant with soybeans?
I came up with 52
Is this correct?
easier way:
the ratio of soybeans : wheat = 2 : 7
let the number of acres of soybeans be 2x
let the number of acres of wheat be 7x
2x + 7x = 270
9x = 270
x = 30
so acres of soybeans = 2(30) = 60
acres of wheat = 7(30) = 210
7(2+3x)+8
To find the number of acres the farmer should plant with soybeans, we need to solve the system of equations:
w + s = 270 (Equation 1)
7s - 2w = 0 (Equation 2)
Let's solve the system using the method of substitution:
From Equation 1, we can express w in terms of s as w = 270 - s.
Substituting this value of w into Equation 2, we get:
7s - 2(270 - s) = 0
7s - 540 + 2s = 0
9s - 540 = 0
9s = 540
s = 540/9
s = 60
Therefore, the farmer should plant 60 acres with soybeans.
So, your answer of 52 acres is incorrect. The correct answer is 60 acres.
To find the number of acres the farmer should plant with soybeans, we need to solve the given system of equations:
w + s = 270
7s - 2w = 0
There are multiple ways to solve this system of equations. One common method is substitution.
We can start by solving the first equation for w in terms of s:
w = 270 - s
Now substitute this expression for w into the second equation:
7s - 2(270 - s) = 0
Expand the equation:
7s - 540 + 2s = 0
Combine like terms:
9s - 540 = 0
Add 540 to both sides:
9s = 540
Divide both sides by 9:
s = 60
So the farmer should plant 60 acres with soybeans.
Therefore, your answer of 52 acres for soybeans is incorrect. The correct answer is 60 acres.