Final answer:
To administer 2.5 mg of gentamicin intravenously, you would need to use 0.25 ml of the injection containing 20 mg of gentamicin in each 2 ml.
Step-by-step explanation:
To determine how many millilitres of the injection should be used, we can set up a proportion based on the ratio of gentamicin in the injection and the desired dose.
We know that the injection contains 20 mg of gentamicin in each 2 ml, so the ratio can be expressed as 20 mg/2 ml. On the other hand, the prescription calls for 2.5 mg of gentamicin to be administered intravenously. So the ratio for the desired dose would be 2.5 mg/x ml, where x represents the number of millilitres we need to find.
We can set up the proportion as follows:
20 mg/2 ml = 2.5 mg/x ml
To solve for x, we can cross-multiply and divide:
20 mg * x ml = 2.5 mg * 2 ml
x ml = (2.5 mg * 2 ml) / 20 mg
x ml = 0.25 ml
So, to administer 2.5 mg of gentamicin, you would need to use 0.25 ml of the injection.