You are a farmer and want to spend under $35,000 on farm equipment. You need a hay baler that costs $6,250 and several plowing disks cost $2,500 each. Write an inequality that models how many plowing disks could be purchased within your budget. What is the maximum number of plowing disks you can buy? Responses A 2,500x + 6,250 < 35,000; 11 plowing disks2,500x + 6,250 < 35,000; 11 plowing disks B 2,500x + 6,250 ≤ 35,000; 11 plowing disks2,500x + 6,250 ≤ 35,000; 11 plowing disks C 2,500x + 6,250 < 35,000; 12 plowing disks2,500x + 6,250 < 35,000; 12 plowing disks D 2,500x + 6,250 ≤ 35,000; 12 plowing disks
The correct inequality that models how many plowing disks could be purchased within the budget is 2,500x + 6,250 ≤ 35,000, where x represents the number of plowing disks.
To find the maximum number of plowing disks that can be bought within the budget, we solve the inequality for x:
2,500x + 6,250 ≤ 35,000
2,500x ≤ 35,000 - 6,250
2,500x ≤ 28,750
x ≤ 28,750/2,500
x ≤ 11.5
Since we cannot have a fraction of a plowing disk, the maximum number of plowing disks that can be bought within the budget is 11 plowing disks.
Therefore, the correct response is A: 2,500x + 6,250 < 35,000; 11 plowing disks.