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?
how do uyou solve this by defining variables and using substitution?
240-80 = 160 acres Sunflowers
= 80 acres flax
Let's assume the number of acres of flax that the farmer plants is 'x'.
According to the given information, the farmer wants to plant 80 more acres of sunflowers than that of flax. So, the number of acres of sunflowers planted will be 'x + 80'.
The total number of acres on the farm is 240 acres. So, the equation can be written as:
x + (x + 80) = 240
By simplifying the equation, we get:
2x + 80 = 240
Subtracting 80 from both sides of the equation, we have:
2x = 160
Dividing both sides by 2, we get:
x = 80
Hence, the farmer needs to plant 80 acres of flax and (80 + 80) = 160 acres of sunflowers.
To find out how many acres of each crop the farmer needs to plant, we can set up a system of equations.
Let's say x represents the number of acres of flax the farmer needs to plant.
Then, the number of acres of sunflowers the farmer needs to plant would be x + 80 (since he wants to plant 80 more acres of sunflowers than flax).
According to the problem, the total area of the farm is 240 acres. So, we can set up the equation:
x + (x + 80) = 240
Now, we can solve this equation to find the value of x.
Combining like terms, the equation becomes:
2x + 80 = 240
Next, we can isolate the term with x by subtracting 80 from both sides:
2x = 160
Dividing both sides by 2, we get:
x = 80
So, the farmer needs to plant 80 acres of flax.
To find the number of acres of sunflowers, we substitute the value of x back into the expression x + 80:
80 + 80 = 160
Hence, the farmer needs to plant 80 acres of flax and 160 acres of sunflowers.