Step 1 :The problem is asking for the volume of Demerol to be administered to the patient. To find this, we need to set up a proportion to compare the dosage ordered by the physician (65 milligrams) to the dosage provided on the Demerol label (60 milligrams in 2 milliliters).
Step 2 :The proportion can be set up as follows: \(\frac{65 \text{ milligrams}}{x \text{ milliliters}} = \frac{60 \text{ milligrams}}{2 \text{ milliliters}}\)
Step 3 :We can solve this proportion for x to find the volume of Demerol to be administered.
Step 4 :The volume of Demerol to be administered is approximately 2.17 milliliters.
Step 5 :Final Answer: The volume of Demerol to be administered should be approximately \(\boxed{2.17}\) milliliters.