12. A nurse is administering a total of 70 milligrams of medication to two patients. The dosage for Patient A must be 2.5 × the dosage for Patient B. Which of the following dosages should be administered to Patient A?
Answer: B
Patient A should receive 50 milligrams of medication.
To determine the dosage for Patient A, we need to set up an equation based on the relationship between the dosages for Patient A and Patient B. Since the dosage for Patient A is 2.5 times that of Patient B, and the total is 70 milligrams, this leads us to the conclusion that Patient A should receive 50 milligrams.
A) 20 mg
If Patient A receives 20 milligrams, this means Patient B would receive 70 mg - 20 mg = 50 mg. However, since 20 mg is not 2.5 times 50 mg (in fact, it is one-fifth), this option does not satisfy the dosage requirement.
B) 50 mg
Administering 50 milligrams to Patient A means Patient B would receive 70 mg - 50 mg = 20 mg. In this case, 50 mg is indeed 2.5 times 20 mg, fulfilling the requirement perfectly. Therefore, this option is correct.
C) 28 mg
If Patient A receives 28 milligrams, then Patient B would get 70 mg - 28 mg = 42 mg. Here, 28 mg is not equal to 2.5 times 42 mg, making this option incorrect as it fails to meet the required dosage ratio.
D) 56 mg
Should Patient A be given 56 milligrams, Patient B would only receive 70 mg - 56 mg = 14 mg. In this scenario, 56 mg is not 2.5 times 14 mg (it's actually 4 times), leading to the conclusion that this option is also incorrect.
Conclusion
The correct dosage of 50 milligrams for Patient A aligns perfectly with the requirement that it is 2.5 times the dosage for Patient B, which would be 20 milligrams. All other options fail to meet the necessary dosage ratio stipulated in the question, confirming that Option B is definitively correct.