a farmer grows corn, tomatoes, and sunflowers on a 320 acre farm. this year the farmer wants to plant twice as many acres of tomatoes as sunflowers. The farmer also wants to plant 40 more acres of corn than of tomatoes. How many acres of of each crop should the farmer plant?
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Let's assign variables to represent the number of acres for each crop.
Let:
x = acres of corn
y = acres of tomatoes
z = acres of sunflowers
We are given the following information:
1. The sum of all acres is equal to 320 acres:
x + y + z = 320
2. The number of acres of tomatoes should be twice the number of acres of sunflowers:
y = 2z
3. The number of acres of corn should be 40 acres more than the number of acres of tomatoes:
x = y + 40
Now we can solve the system of equations.
From equation 2, we substitute y = 2z into equation 3:
x = (2z) + 40
Now we substitute the values of x and y from equations 2 and 3 into equation 1:
(2z) + 40 + 2z + z = 320
Simplifying the equation:
5z + 40 = 320
5z = 320 - 40
5z = 280
z = 280 / 5
z = 56
Substituting the value of z back into equation 2:
y = 2z
y = 2(56)
y = 112
Substituting the value of z back into equation 3:
x = y + 40
x = 112 + 40
x = 152
Therefore, the farmer should plant 152 acres of corn, 112 acres of tomatoes, and 56 acres of sunflowers.
To solve this problem, we can break it down into smaller steps and use algebraic expressions to represent the information given.
Let's denote the number of acres of sunflowers as 'x'.
We know that the farmer wants to plant twice as many acres of tomatoes as sunflowers. So, the number of acres of tomatoes would be 2x.
Additionally, the farmer wants to plant 40 more acres of corn than of tomatoes. So, the number of acres of corn would be 2x + 40.
Now, we are given that the total area of the farm is 320 acres. So, we can create an equation representing the sum of the acres of each crop:
x + 2x + (2x + 40) = 320
Simplifying the equation, we have:
5x + 40 = 320
Subtracting 40 from both sides:
5x = 280
Dividing both sides by 5, we find:
x = 56
Therefore, the farmer should plant 56 acres of sunflowers, 2 * 56 = 112 acres of tomatoes, and 2 * 56 + 40 = 152 acres of corn.
Let s = acres of sunflowers
s + 2s + 2s + 40 = 320
5s = 280
s = 56