I need help with pharmacy math, more specifically, Algorithms?

Question

Any help would be greatly appreciated!
Here is the problem (it's long):

You need to prepare a topical solution with a final product.  Prepare a 1 liter IV bag with a 27% concentration of product x.  The strengths available are 50%, 70%, and 10%.
Questions:
1) How many parts of the 10% solution will be required?
2) How many parts of the 70% solution will be required?
3) How many parts of the 50% solution will be required?
4) If the final product is to be a total volume of 1 liter how many milliliters of the 10% solution will be required?
5) If the final product is to be a total volume of a liter how many milliliters of the 50% solution will be required?
6) If the final product is to be a total volume of a liter how many milliliters of the 70% solution will be required?

daddyrx · Accepted Answer

You only need 2 of the solutions. One greater than 27% and one less than 27%. I choose 10% and 50% so my answer to question #2 is 0 parts and question #6 is 0ml.

This is a classic alligation problem. Ignore the dots.

50................ 17parts (27-10)
.........27.....................[final concentration]
10................ 13parts (50-27)
.................... ----------
.................... 30parts total

All that means is your final solution will need 17parts of 50% and 13parts of 10%. [this answers 1 and 3]

Now the math....
You need to make 1000ml which equals 30parts
1000ml/30parts = 33,33ml/part

How much 50%: 33.33ml/part * 17parts = 566.61ml [answers #5]
How much 10%: 33.33ml/part * 13parts = 433.39ml [answers #4]

PS: You can also do it using the 70% and 10%. Same procedure.

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I need help with pharmacy math, more specifically, Algorithms?

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