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?

Question

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?

Answer 1

Let's denote the maximum number of plowing disks that can be purchased as x. Since each plowing disk costs $2,500 and the hay baler costs $6,250, the total amount of money spent on plowing disks would be 2,500x dollars.

To ensure that the total spending, including the hay baler and plowing disks, is less than or equal to $35,000, the inequality can be written as:

2,500x + 6,250 ≤ 35,000

Simplifying the inequality:

2,500x ≤ 35,000 - 6,250
2,500x ≤ 28,750

To find the maximum value for x, we divide both sides of the inequality by 2,500:

x ≤ 28,750 / 2,500
x ≤ 11.5

Since we can only purchase a whole number of plowing disks, the maximum number of plowing disks that can be bought while staying within the budget is 11.