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 answer is C) 2,500x + 6,250 < 35,000; 12 plowing disks.
To determine the maximum number of plowing disks that can be bought within the budget, we need to find the maximum value of x in the inequality.
Since each plowing disk costs $2,500 and there are a total of $35,000 available to spend, the inequality becomes:
2,500x + 6,250 < 35,000
Subtracting 6,250 from both sides:
2,500x < 28,750
Dividing both sides by 2,500:
x < 11.5
Since x represents the number of plowing disks, it is not possible to purchase a fractional amount. Therefore, the maximum number of plowing disks that can be bought is 11.