Farmer Brown planted corn and wheat on his 450 acres of land. The cost of planting and harvesting corn is $280.00 per acre. The cost of planting and harvesting wheat is $125.00 per acre. If Farmer Brown's total cost was $102,750, how many acres of corn did he plant?
W = 450 - C
280C + 125W = 102,750
Substitute 450-C for W in the second equation and solve for C.
To find out how many acres of corn Farmer Brown planted, we need to set up an equation based on the given information.
Let's assume that Farmer Brown planted x acres of corn.
The total cost of planting and harvesting corn on x acres is $280.00 per acre. So, the cost of planting and harvesting x acres of corn would be 280 * x = 280x.
Farmer Brown also planted wheat on the remaining land, which is 450 - x acres. The cost of planting and harvesting wheat is $125.00 per acre. So, the cost of planting and harvesting (450 - x) acres of wheat would be 125 * (450 - x) = 56250 - 125x.
We are given that the total cost was $102,750. So, we can set up the equation:
280x + 56250 - 125x = 102750
To solve this equation, we need to combine like terms:
155x + 56250 = 102750
Next, we can subtract 56250 from both sides of the equation:
155x = 102750 - 56250
155x = 46500
Finally, we can divide both sides by 155 to find the value of x:
x = 46500 / 155
x = 300
Therefore, Farmer Brown planted 300 acres of corn.