Question

1. farming 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?

Explanation:

Step1: Define variables

Let \( x \) be the number of acres of pumpkins. Then the number of acres of corn is \( x + 250 \).

Step2: Set up equation

The total number of acres is 420, so the sum of acres of pumpkins and corn is 420. So we have the equation:
\( x+(x + 250)=420 \)

Step3: Solve the equation

First, simplify the left - hand side: \( 2x+250 = 420 \)
Subtract 250 from both sides: \( 2x=420 - 250=170 \)
Divide both sides by 2: \( x=\frac{170}{2}=85 \)

Step4: Find acres of corn

The number of acres of corn is \( x + 250=85 + 250 = 335 \)

Answer:

The farmer should plant 85 acres of pumpkins and 335 acres of corn.