25. A bag of dog food weighs 40 pounds. The amount of food in the bag is more than 3 × the amount needed to feed a dog for one week. Which inequality can be used to determine the possible values for p, the pounds of food needed to feed the dog for one week?
Answer: D
3p > 40
The inequality that can be used to determine the possible values for p, the pounds of food needed to feed the dog for one week, is 3p > 40. This indicates that the total amount of food required for three weeks exceeds the weight of the bag of dog food.
A) p < 3(40)
This option incorrectly suggests that the amount of food needed for one week is less than three times the weight of the bag. Since the problem states that the bag contains more than three weeks' worth of food, this inequality does not accurately represent the relationship.
B) 3p < 40
This inequality implies that three times the weekly food requirement is less than the total bag weight. This is incorrect because the bag contains more than this amount, hence it does not satisfy the conditions set by the problem.
C) p > 3(40)
This option suggests that the weekly food requirement is greater than three times the bag's weight. This is incorrect, as it contradicts the problem statement, which indicates that the bag contains more than three times the weekly amount, not less.
D) 3p > 40
This inequality correctly represents the situation described in the problem. It shows that the total food needed for three weeks (3p) is greater than the 40 pounds available in the bag, aligning with the condition that the bag holds a surplus of food for that time period.
Conclusion
The correct inequality, 3p > 40, accurately reflects the relationship between the amount of food in the bag and the weekly requirement for the dog. All other options misinterpret the quantities involved, thus failing to provide a valid mathematical representation of the scenario outlined in the question.