A farmer grows only pumpkins and corn on her 420-acre farm. This year she wants to plant 250 more acres of corn than pumpkins. How many acres of each crop should the farmer plant?
x+(x+250)=420
2x+250=420
x=85
85+250=335
Therefore,
335 acres of corn and 85 acres of pumpkins
To determine the number of acres of each crop the farmer should plant, we can set up a system of equations based on the information provided.
Let's assume that the number of acres of pumpkins the farmer plants is represented by 'p', and the number of acres of corn is represented by 'c'.
According to the problem, the farmer has a total of 420 acres of land available to plant crops. Therefore, the first equation is:
p + c = 420 (Equation 1)
The problem also states that the farmer wants to plant 250 more acres of corn than pumpkins. We can express this relationship in the second equation:
c = p + 250 (Equation 2)
Now we have a system of equations:
p + c = 420 (Equation 1)
c = p + 250 (Equation 2)
We can solve this system of equations to find the values of 'p' and 'c'. One way to do this is by substituting Equation 2 into Equation 1:
p + (p + 250) = 420
Simplifying the equation:
2p + 250 = 420
Subtracting 250 from both sides:
2p = 420 - 250
2p = 170
Dividing both sides by 2:
p = 85
Now we have the value of 'p' (pumpkins). To find the value of 'c' (corn), we can substitute the value of 'p' into Equation 2:
c = 85 + 250
c = 335
Therefore, the farmer should plant 85 acres of pumpkins and 335 acres of corn.
335 acres of corn
85 acres of pumpkins