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Concentration percentage math

by Amy

How many grams of 2.5% hydrocortisone cream should be mixed with 30 gram of 1% hydrocortisone cream to make 1.5% hydrocortisone cream?

Comments for Concentration percentage math

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I am a pharmacist and this is a pretty difficult question
by: John T.

I have been practicing for 5 years and I would NEVER expect a technician to be able to do this but here is the answer using an alligation:
(this is difficult to do in a text-only fashion so I will try my best to explain it)

In the middle of the alligation is the 1.5% cream you are trying to make. The top left number is the 2.5% cream you have, bottom left is the 1% cream. Top right is 0.5 (which is 1.5-1), bottom right is 1 (which is 2.5-1.5). This gives a total of 1.5 parts for the final volume of 1.5% cream. The 30g of 1% cream you start with represents 1 part. Because you know that the TOTAL volume of 1.5% cream is made up of 1.5 parts, then you need exactly 1/2 that amount (or 0.5 parts) of 2.5% cream which would be 15 grams.

TO CHECK THIS ANSWER:
Calculate the raw amount of active drug that is in both the 1% and 2.5% creams and make sure it adds up to 1.5%. For the 1% cream: 0.01x30g=0.3g of active drug. For the 2.5% cream: 0.025x15g=0.375g of active drug. This gives a total of 0.675g. Now set up a proportion and solve for X:
(the 45 comes from the total amount of cream, 30g + 15g)
1.5g/100g = X/45g
X=0.675
Hope this was clear.
I'm a technician.
by: Anonymous

I got 10g of the 2.5% and 20g of the 1%

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