6. A doctor writes a prescription for 20 mg of Tobramycin antibiotic saline solution. The solution is to be injected intravenously one time a day. On hand we have a 30 mg/2 ml vial of Tobramycin.
To determine how much of the 30 mg/2 ml vial of Tobramycin antibiotic saline solution to use for the prescription, we need to calculate the volume of the solution that contains the desired dose.
Here's how to do it:
1. Start by converting the prescribed dose, 20 mg, to the same units as the concentration of the vial. In this case, we have milligrams (mg) as the unit, which matches the concentration of the vial.
2. Next, use the concentration of the vial to determine how many milliliters (ml) of solution contain the prescribed dose. Since the concentration is 30 mg per 2 ml, we can set up a proportion to find the volume:
(20 mg) / (x ml) = (30 mg) / (2 ml)
Cross-multiply and solve for x:
20 mg * 2 ml = 30 mg * x ml
40 mg ml = 30 mg x ml
Divide both sides by 30 mg to isolate x:
x ml = (40 mg ml) / (30 mg)
x ml = 4/3 ml
Therefore, the prescribed dose of 20 mg of Tobramycin requires approximately 4/3 ml of the solution.
3. Since it's not practical to measure a fraction of a milliliter accurately, round the result to an appropriate measurement increment. In this case, we can round it to 1 ml.
Hence, you would use approximately 1 ml of the 30 mg/2 ml vial of Tobramycin antibiotic saline solution for the prescribed dose of 20 mg.