Final answer:
Old MacDonald's farm's width, given the perimeter of at most 220 feet and length being three times the width, is at most 27.5 feet. The inequality modeling this situation is D. 2(3W) + 2W ≤ 220.
Step-by-step explanation:
The problem presented is modeling an inequality related to the perimeter of a rectangular farm. Old MacDonald's farm has a length three times its width, and the perimeter is at most 220 feet. To express this mathematically, the perimeter P can be represented as:
P = 2L + 2W
Where L is the length and W is the width. Considering the relationship between length and width given by L = 3W, we can rewrite this equation as:
P = 2(3W) + 2W
Following the condition that the perimeter is at most 220 feet, our inequality becomes:
2(3W) + 2W ≤ 220
Simplifying, we have:
6W + 2W ≤ 220
8W ≤ 220
Dividing both sides by 8:
W ≤ 27.5
Thus, the greatest possible value for the width is 27.5 feet. The inequality that models this problem is D. 2(3W) + 2W ≤ 220, which is the correct representation of the perimeter's restriction for the farm.