Drug Math Question

Vancomycin 750mg in 15ml. Drug book says to dilute to 2.5-5mg/ml. How do you get up and solve?

This is what I have done:

750mg x (ml/5mg)= 150ml

150ml- 15ml=135ml

So I should add the 750mg Vanc/15ml NS to 135ml NS?

I'm not sure of the question you are asking. Is there an order for 750mg Vanco diluted in 15 mL NS? Shouldn't it be what's available, not the drug book?

Vancomycin 750mg in 15ml. Drug book says to dilute to 2.5-5mg/ml. How do you get up and solve?

I've never encountered any question like this before. Are you sure it's asking how much to add to the available Vancomycin 750mg/15ml so that the concentration goes down to 2.5-5mg/ml?

If so, this is how I solved it - by proportion. I made 2 separate equations because the given end concentration is a range, so you have to come up with a range of volumes to add to the preexisting solution.

To get down to 2.5mg/ml: 2.5 mg/ml = 750mg / (15ml + x)

Cross multiplying, you have:

750 mg*ml = 2.5 mg (15 ml + x)

750 mg*ml = 37.5 mg*ml + 2.5 mg*x

Subtract both ends of the equation by 37.5 mg*ml:

2.5 mg*x = 750 mg*ml - 37.5 mg*ml

2.5 mg*x = 712.5 mg*ml

Divide both ends of the equation by 2.5 mg so you can get x:

x = 285 ml

Do the same equation all over, except now, use 5mg/ml as your end concentration. This will give you x = 135 ml

So, to get to a concentration of 2.5 mg/ml, you add 285 ml to your existing solution. To get to 5 mg/ml, you add 135 ml.

Yes, you are correct.

The question is telling you that you need to dilute the Vancomycin with saline until you get a certain concentration of the medication.

To calculate the medication concentration, divide the total dose by the total amount of fluid.

Vancomycin 750mg / 15 ml = 50 mg/mL is your current concentration

You need a concentration of at least 5 mg/mL.

Do find that concentration, it's very simple. Just divide the total dose by the concentration that you wish to achieve.

Vancomycin 750 mg / final concentration of 5mg/mL = 150 mL.

Since you already have 15 mL, you can add 135 mL to give you a total of 150 mL and a final concentration of 5mg/mL.

To double check yourself, do the first step again. Vancomycin 750 mg / 150mL = 5 mg/mL