Final answer:
To determine how many acres of corn Farmer Brown planted, we set up and solved a system of equations using the given costs per acre and the total cost. The equations yielded a result of approximately 925 acres of corn planted.
Step-by-step explanation:
We can solve Farmer Brown's problem using a system of linear equations. Let's denote the number of acres of corn planted as x and the number of acres of wheat farmed as y. Since the total land is 1180 acres, we have the equation x + y = 1180. We also know the costs for planting and harvesting: $270 per acre for corn and $135 per acre for wheat. Multiplying the number of acres by the respective costs, we get another equation based on the total cost of $249,750: 270x + 135y = 249,750.
To find the number of acres of corn planted, we solve this system of equations. We can first multiply the second equation by 2 to eliminate y as follows: 2(270x) + 2(135y) = 2(249,750) simplifying to 540x + 270y = 499,500. Now subtract the first equation from this to remove y: (540x + 270y) - (270x + 135y) = 499,500 - 249,750. This yields 270x = 249,750.
Finally, divide both sides by 270 to find x: x = 249,750 / 270, which equals about 925 acres. Therefore, Farmer Brown planted roughly 925 acres of corn.