Med Math Question..

Daytonite, BSN, RN · Sep 5, 2007

order: vibramycin 230 mg per 1000 ml normosol-m in d5w iv to run in 24 hours.

label: vibramycin 100 mg.

directions for reconstitution: add 10 ml sterile water for injection to yield a concentration of 10 mg/ml.

how much of the reconstituted solution must be added to the iv bottle to provide the ordered dose of vibramycin 230 mg?

if your reconstituted vial of vibramycin gives you 10 mg/ml and you want to put 230 mg of the vibramycin in an iv bag then this is a problem of ratios:

10 mg/1 ml

(what you have on hand) =

230 mg/x ml

(what you need to add to the iv bag). solve for

x

by cross multiplying and factor out the labels. this gives you this equation:

10x = 230

. divide both sides of the equation by 10 and

x = 23

. if you substitute that back into your original ratio you have an answer of

10 mg/1 ml = 230 mg/

23

ml

what this answer means is that you will want to add 23 ml of the reconstituted vibramycin to the 1000 ml of d5normosol-m. since each vial contains 10 ml

23/10 = 2.3

which means you need 2.3 vials of the vibramycin. however, in the practical world there is no such thing as a 0.3 of a vial. so, you would reconstitute 3 vials of the vibramycin, pull up the 23 ml you need from them and discard the unused amount.

the physician orders 500 ml of d5w to infuse @ 10 drops per minute. the infusion set you have delivers 20 drops per ml. how long will it take for the iv to infuse in hours?

the trick here is how you set up the numerators and denominators of the relationships. you want to end up with "

hours

" in the numerator of the final answer.

500 ml/1

(dose desired)

x 1 minute/10 gtts

(drip rate/infusion rate)

x 20 gtts/1 ml

(drop factor of iv tubing)

x 1 hour/60 minutes

(conversion factor)

=

16.6 hours

MikeyJ, RN · Sep 5, 2007

Thanks so much Daytonite! The second one I see where I went wrong -- I set it up right. The first one (reconstitution) still baffles me. I am not sure if it is just the wording of the problem or what.

mysterious_one, ASN, RN · Sep 5, 2007

I set up the first problem like this:

you have:

LABEL: Vibramycin 100 mg.

DIRECTIONS FOR RECONSTITUTION: Add 10 mL sterile water for injection to yield a concentration of 10 mg/mL.

so you need 10 ml to get a 100mg of Vibr., because : 10mg/ml, ok.

but you want 230 mg.

So set it up in a proportion

100mg = 10ml

230mg = ?

now crossmultiply and then divide

230 x 10 = 2300 / 100 = 23ml

I still have problems with the second problem you gave, I don't quite understand how Daytonite set it up, and I can't figure out an easy way myself , so if anyone has any suggestions , share them please:D, thanks

Jado0114 · Sep 5, 2007

2nd problem: formula

V x DF (drop factor) = gtts/min

T

Fill in formula with info you already have, like this:

500 ml x 20 gtts/ml = 10 gtts/min

T

In order to ISOLATE the "T" which stands for Time, you need to multiply both sides by "T".

T x 500 ml x 20 gtts/ml = 10 gtts/min x T

T

"T"s on left side cancel each other out leaving you with 500 x 20 = 10,000

Right side is 10 x T (10T)

So you have 10,000 = 10T....now divide both sides by 10.

10,000 = 10T

10 10

You get 1000...but this is in minutes. You need to DIVIDE by 60 to get hours.

1000/60 = 16.666 (round to hundredths) 16.67 hrs

(the .67 is not minutes)

You need to take the 0.67 (of the 16.67) and MULTIPLY by 60 to get minutes (if you need the minutes too) 0.67 x 60 = 40.2 min

So your answer is 16 hours 40 minutes.

I hope I haven't confused you!!!!

Daytonite, BSN, RN · Sep 5, 2007

Thanks so much Daytonite! The second one I see where I went wrong -- I set it up right. The first one (reconstitution) still baffles me. I am not sure if it is just the wording of the problem or what.

My old algebra instructors always said that when we were having trouble figuring out word problems to draw a picture. The problem tells you "Add 10 mL sterile water for injection to yield a concentration of 10 mg/mL." This means to add 10 mL sterile water for injection to yield a concentration of 10 mg/mL toeach vial of Vibramycin. It comes is small glass bottles (vials) of powder containing 100 mg of Vibramycin. You need to add 10 mL of sterile water to each vial to reconstitute it. Make 3 rectangles on a blank piece of paper. Label each "100 mg". Next add "10 mL" underneath each label of "10 mg". You need 230 mg, right? You can visually see that it is going to take 2 full vials (100 mg + 100 mg = 200 mg) plus some more from the third vial. Since the problem very nicely tells you that there is 10 mg/1 mL and you need 30 mg more, how many mL do you need to take out of the third vial? Again, you can do a ratio to come up with the 3 mL. This gives you your grand total of 23 mLs.

Here is the actual insert from Pfizer, the manufacture of Vibramycin, that comes with the drug (http://www.pfizer.com/pfizer/download/uspi_vibramycin_injection.pdf). I was hoping it would have a picture of a vial on it, but it doesn't. Toward the bottom, on page 7, are the directions for reconstitution. They are just like your problem.

In actual practice you would have these three vials in front of you and would see this. Unless you don't have your brain engaged, it's kind of hard not to realize when you are staring at 100 mg vials that 2+ of them make up the 230 mg that you are going to need. Then it becomes of matter of how much to pull out of the last vial.

mysterious_one, ASN, RN · Sep 5, 2007

2nd problem: formula
V x DF (drop factor) = gtts/min
T
Fill in formula with info you already have, like this:
500 ml x 20 gtts/ml = 10 gtts/min
T
In order to ISOLATE the "T" which stands for Time, you need to multiply both sides by "T".
T x 500 ml x 20 gtts/ml = 10 gtts/min x T
T
"T"s on left side cancel each other out leaving you with 500 x 20 = 10,000
Right side is 10 x T (10T)
So you have 10,000 = 10T....now divide both sides by 10.
10,000 = 10T
10 10
You get 1000...but this is in minutes. You need to DIVIDE by 60 to get hours.
1000/60 = 16.666 (round to hundredths) 16.67 hrs
(the .67 is not minutes)
You need to take the 0.67 (of the 16.67) and MULTIPLY by 60 to get minutes (if you need the minutes too) 0.67 x 60 = 40.2 min
So your answer is 16 hours 40 minutes.
I hope I haven't confused you!!!!

thanks , this helped me to see it clearer, I did forget one step, that's why I didn't get it.

MikeyJ, RN · Sep 6, 2007

2nd problem: formula
V x DF (drop factor) = gtts/min
T
Fill in formula with info you already have, like this:
500 ml x 20 gtts/ml = 10 gtts/min
T
In order to ISOLATE the "T" which stands for Time, you need to multiply both sides by "T".
T x 500 ml x 20 gtts/ml = 10 gtts/min x T
T

"T"s on left side cancel each other out leaving you with 500 x 20 = 10,000
Right side is 10 x T (10T)
So you have 10,000 = 10T....now divide both sides by 10.
10,000 = 10T
10 10
You get 1000...but this is in minutes. You need to DIVIDE by 60 to get hours.
1000/60 = 16.666 (round to hundredths) 16.67 hrs
(the .67 is not minutes)
You need to take the 0.67 (of the 16.67) and MULTIPLY by 60 to get minutes (if you need the minutes too) 0.67 x 60 = 40.2 min

So your answer is 16 hours 40 minutes.

I hope I haven't confused you!!!!

Oddly, I had gotten 16.4 as well... but my professor counted it as wrong. Daytonite came up with the answer 16.6, so i assume that is the right answer.

MikeyJ, RN · Sep 6, 2007

Thanks for everyone's help! I re-took the math competency quiz tonight because I had to get those two questions right, and even though the quiz had slightly different scenarios and different numbers, I was able to get those two types of problems right. Thanks again!!! :)

Finally2008 · Sep 6, 2007

the trick here is how you set up the numerators and denominators of the relationships. you want to end up with "hours" in the numerator of the final answer.
500 ml/1
(dose desired)
x 1 minute/10 gtts
(drip rate/infusion rate)
x 20 gtts/1 ml
(drop factor of iv tubing)
x 1 hour/60 minutes
(conversion factor)
=
16.6 hours

i love figuring out problems now with dimensional analysis! this is the best way to do math problems. :)