Please Help Math Exam Retake Tomorrow Struggling

Then set up the dimensional analysis so that "units" cancel and mL is left for the answer:
Please help.... I have asked and asked and cannot get a clear answer on how you "choose" the correct range of diluent in these kinds of questions. I assumed you pick the range closest to the order which would be 250,000, but the answer key says the correct choice is 200,000. I have to retake the math exam tomorrow to get into clinical and I am struggling with this type of question.... I am having the same problem with insulin and heprin... I cannot understand how to pick the right range of concentration for each question.... I am not having a problem with the DA math equations but with picking ranges... Please help... is there a RULE ?
Example
The order is to give 300,000 units of Penicillin G Potassium IM. A concentration of 200,000 units/ml should be used. The medication on hand is in a 1,000,000 unit vial. How many mL will you give?
Here are typical instructions for reconstitution of medication
supplied in a 1,000,000 unit vialConcentration Diluent to be Added 100,000 units/ml 200,000 units/ml 250,000 units/ml 9.6 ml4.6 ml3.6 ml According to these instructions, you should add 4.6 mL of dilutent to the stock penicillin.The reconstitution process.
Ans: 1.5 mLLast edit by Kat710 on Oct 20, '13 

Oct 20, '13Why are you confused? The question tells you what concentration to use. There are 5mL in the vial. It says what concentration you have.

Oct 20, '13Because this question is from a math help site, she is just stating what to use, but not saying why. Normally that part would not be included within the question. On my previous math exam there were several of these questions but "you" had to choose the correct dilution ratio... this is where I am lost. Even in my two nursing math books they work the problems out for you, but none of the books tell why or how they choose a particular dilution ratio....

Oct 20, '13I was told to use less diluent for IM injection for less total volume because the muscle can only hold so much and IV the larger range of diluent would be used... but if you look at this problem it is neither... it is right in the middle... I am very confused and wish someone could tell me the rule of thumb.

Oct 20, '13Quote from Kat710I believe 1.5 mL is okay for large muscles. But I may be wrong.I was told to use less diluent for IM injection for less total volume because the muscle can only hold so much and IV the larger range of diluent would be used... but if you look at this problem it is neither... it is right in the middle... I am very confused and wish someone could tell me the rule of thumb.
Also, there is no rule of thumb. You use the ratio that they tell you to use. You can't make up your own concentration. 


Oct 20, '13Yes.... that is what all of our books say too.. they specify a range according to IM or IV or Subcut injection...on the label...However, we are told this is to challenge our critical thinking...

Oct 21, '13Ok.....
Ordered: 300,000 units
On hand: 200,000 units/ml
Equation: 300,000 / 200,000 X 1 ml = 1.5 mL to give
The question ask how many mL to give. The instruction indicates a 4.6 mL diluent is to be used with a concentration of 200,000 units/mL. The diluent does not change the initial amount of the concentration. If I am incorrect, someone please correct me.
You are adding to the concentration not what was ordered. Some questions add additional information that may throw you off. Always look at what the question is truly asking you. It should be at the end of the question. Best wishes on your exam.
Also, I believe 1.5 mL is a safe amount for large muscles too.Last edit by teacher08 on Oct 21, '13 
Oct 21, '13Thank you for the help and the best wishes. I appreciate it. I guess the question looks confusing because I posted the teachers guides in there.. The question normally would not have indicated 4.6ML... most of the questions we are getting on the tests ask "us" to pick the right diluent based on the order and it is never exact.
So the question would read like this:
Example
The order is to give 300,000 units of Penicillin G Potassium IM. The medication on hand is in a 1,000,000 unit vial. How many mL will you give?
Concentration Diluent to be Added 100,000 units/ml
200,000 units/ml
250,000 units/ml9.6 ml
4.6 ml
3.6 ml

Oct 21, '13We would have to know which diluent concentration to pick... Most labels will state which one to use for IM or IV, the tests questions are not giving us that and like this question they are not giving us an exact match either, only ranges... and we have to choose which one is appropriate.

Oct 21, '13That's the actual question? Wow, I can see why you would be confused with which diluent to select especially without any indication of what concentration is available. However, if the picture is included with the math problem, it illustrates 4.6 mL diluent and therefore you would select 200,000 units and solve and end up with 1.5 mL. No picture.....no answer for diluent.
I've always been taught with reconstitution to locate the directions on the label to identify the type and volume of mandatory diluent. It's not a guessing game or a critical thinking situation in my opinion...it's called follow the manufacture's specific directions very carefully and get another nurse to verify.
However, critically thinking (in my opinion for my instructor) would indicate the final question in the math problem still remains the same how many ML would you give and I know 1.5 mL is safe for large muscles. Its also the correct answer with the illustration.
I hate tricky questions. However, we do learn from them and they will make us think.
Don't worry to much you'll ace the exam!Last edit by teacher08 on Oct 21, '13 
Oct 21, '13If the bottle tells you that adding 4.6cc to it makes a total of 5cc with a concentration of 200K units/cc, then that is true for that drug and that's what you work with.
Another drug might tell you to add 3.9cc for a total of 6cc with a concentration of 2mg/cc; then you believe that and proceed accordingly.
Another drug might say to add 9.5cc for a total of 10cc with a concentration of 600mg/cc; then you believe that.
I think what I hear you struggling with is that you are looking for a hardandfast rule about how much diluent to add to any vial to get a volume that is safe to administer via a given route. There is no such rule. What this test question is asking is whether you know what's a safe volume to give IM (2cc is about right for a max in an adult thigh). That's a separate question than how much diluent to mix the drug with; that instruction is given separately on the label or in the setup for the question. In this case, you get 200,000 units per cc and the prescribed dose is 300,000 units, so the dose will be 1.5cc and do you know whether that's safe to give in one IM or not? That's the question.
Hope you did well on your test today!