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?

Rationale

3p > 40

The inequality 3p > 40 accurately represents the relationship between the amount of food in the bag and the weekly food requirement for the dog. Here, p signifies the pounds of food needed for one week, and since the bag contains more than three times that amount, the inequality reflects this relationship.

A (p < 3(40)) YOUR ANSWER

This inequality incorrectly suggests that the amount of food needed for one week is less than three times the total weight of the bag. However, since the bag weighs 40 pounds and contains more than three times the weekly requirement, this does not satisfy the given condition.

B (3p < 40) YOUR ANSWER

This option incorrectly indicates that three times the weekly food requirement is less than the total weight of the bag. This contradicts the information given in the problem, as the bag actually exceeds three times the weekly requirement; thus, this inequality is not appropriate.

C (p > 3(40)) YOUR ANSWER

This inequality suggests that the weekly food requirement exceeds three times the total weight of the bag. This is logically flawed since the bag contains more than three times the requirement, meaning p must be less than that value rather than greater.

D (3p > 40) CORRECT

This is the correct inequality as it accurately captures the relationship stated in the question. It indicates that three times the weekly food requirement (3p) is greater than the total weight of the bag (40 pounds), aligning with the condition provided.

Conclusion

To determine the pounds of food needed to feed the dog for one week, the inequality 3p > 40 must be used. This reflects that the total amount of food in the bag exceeds three times the weekly requirement. The incorrect choices fail to represent the relationship outlined in the question, illustrating the importance of correctly interpreting inequalities in the context provided.

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?

3p > 40

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