Pharmacy Math Dilution problem

by Marlene
(Rye)

What volume in mL of syrup is needed to dilute 100 ml of Amoxicillin 20mg/5ml to a concentration of 2mg/mL ?

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The easy way.
by: Anonymous

You have:
syrup
Amoxicillin 20mg/5ml (100 ml)
You want:
Amoxicillin 2mg/mL

You must calculate: volume of syrup needed

You can treat this as an alligation where one of the mixtures is 0 and the other is 20mg/5ml, which is the same as 4mg/ml

Admittedly, once you state the amoxicillin concentration as 4 mg/ml, the answer is obvious, but follow anyway:

4 2
\ /
2
/ \
0 2

The syrup is mixed with the amoxicillin in a 2:2 ratio, which is the same as a 1:1:ratio, so for 100 ml amoxicillin mixture, dilute with the same amount of syrup: 100 ml.

Now: check the answer
100 ml of syrup+100 ml Amoxicillin mixture =200 ml total
100 ml x 20mg/5ml = 400 mg Amoxicillin
400 mg Amox/200 ml mixture =2mg Amox/ml <- and that's what you need

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