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?

Rationale

Patient A should be administered 50 mg of medication.

To find the correct dosage for Patient A, we can set up an equation based on the relationship between the dosages. If Patient B receives x mg, then Patient A receives 2.5x mg. The total dosage is 70 mg, leading to the equation x + 2.5x = 70, which simplifies to 3.5x = 70, resulting in x = 20 mg for Patient B and 50 mg for Patient A.

A (20 mg) YOUR ANSWER

This dosage represents the amount for Patient B, not Patient A. According to the problem, Patient A must receive 2.5 times the dosage of Patient B. Therefore, 20 mg is not a valid option for Patient A.

B (50 mg) CORRECT

This is the correct answer, as calculated from the equation. Patient A receives 50 mg while Patient B receives 20 mg, maintaining the required ratio of 2.5:1 between their dosages.

C (28 mg) YOUR ANSWER

If Patient A were to receive 28 mg, then Patient B's dosage would need to be calculated as 28 mg / 2.5, which equals 11.2 mg. This results in a total of 39.2 mg, which does not meet the total required dosage of 70 mg.

D (56 mg) YOUR ANSWER

If Patient A receives 56 mg, then Patient B's dosage would be 56 mg / 2.5, which equals 22.4 mg. The total would then be 78.4 mg, exceeding the total dosage of 70 mg, making this option invalid.

Conclusion

The calculation shows that Patient A should receive 50 mg of medication, which is 2.5 times the 20 mg dosage for Patient B. This ensures the total administered dosage is 70 mg, satisfying the conditions set in the question. The other options either misrepresent the relationship of dosages or do not sum to the required total, confirming that 50 mg is the only valid choice for Patient A.

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?

Patient A should be administered 50 mg of medication.

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