Define variable and write a system of equations for this situation. Solve using substitution.
A farmer grows only sunflowers and flax on his 240-acre farm. This year he wants to plant 80 more acres of sunflowers than that of flax. How many acres of each crop does the farmer need to plant?
let the number of acres for flax be f
let the number of acres for sunflowers be s
s + f = 240
f = s - 80
take it from there.
To solve this problem, let's define a variable.
Let's say x represents the number of acres of flax that the farmer needs to plant. Since the farmer wants to plant 80 more acres of sunflowers than flax, we can represent the number of acres of sunflowers as x + 80.
Now, we can write a system of equations based on the given information:
Equation 1: x + (x + 80) = 240
In this equation, we're summing up the acres of flax (x) and acres of sunflowers (x + 80) and setting it equal to the total farm area of 240 acres.
Simplifying Equation 1: 2x + 80 = 240
We've combined like terms by adding x and x together.
Equation 2: x + 80 - x = 0
In this equation, we're calculating the difference between the number of acres of flax (x + 80) and acres of sunflowers (x) and setting it equal to 0. This equation represents the statement that the farmer wants to plant 80 more acres of sunflowers than flax.
Now, we can solve the system of equations using substitution.
From Equation 2, we can see that x + 80 - x = 0. Simplifying this equation, we get 80 = 0, which is not true. Therefore, this system of equations has no solution.
In this case, there is no solution because the equations are contradictory. The information given in the problem is not consistent or possible to achieve.