# Pharmacy Dilution Math

Pharmacy Dilution Math is a process of reducing the concentration of a solution by adding more solvent. The formulas explained here are only to be used for the purpose of diluting a solution from a higher percentage to a lower percentage. These methods are shortcuts to algebra methods and should only be used for taking the pharmacy tech test. A tech who will be compounding solutions should always use the proper algebra formula.

The pharmacist hands you a 1.5L bottle of a 20% solution and asks that you mix it with sterile water to make as much 12% solution as possible. How much sterile water will you use ?

A.   525mL

B.   800mL

C. 1000mL

D. 1250mL

In this video is how to do it using proportions math.

This video shows how to do the same problem, but with
alligation, and basic algebra.

### Another way to do this problem is to use the formula:

C1 X V1 = C2 X V2
C1= Concentration 1
V1= Volume 1
C2= Concentration 2
V2= Volume 2

1) First, plug it all in:

### (.20)(1500ml) = (.12)( X )

(Volume 2 is unknown or "X")

↓   ↓   ↓

2) Do the multiplication

300ml = .12X

↓   ↓   ↓

3) Do the division to isolate X

 300ml .12X .12 .12

↓   ↓  ↓

4) Now you have the larger volume.

(but, this is not the final answer)

2500mL = X

↓   ↓  ↓

5) Figure out the difference between the Smaller
and larger volumes.

2500mL
- 1500mL
--------
1000mL
- would be added to the solution.

If you want to cross check your answer, you could by taking this new information and doing an
Alligation. This type of pharmacy tech math may be more difficult for those who have not taken algebra in school or pharmacy dilution math before.

## Want to see the proper algebra wayto do this problem in text?

Question:
The pharmacist hands you a 1.5L bottle of a 20% solution and asks that you mix it with sterile water to make as much 12% solution as possible. How much sterile water will you use ?

A. 525mL

B. 800mL

C. 1000mL

D. 1250mL

 % Qty decimal Set-up sol. 1 20% 1500ml .20 1500(.20) sol. 2 0% X .00 .00(X) Want 12% 1500 + X .12 (1500 + X)(.12)

1) The Equation Set-up:

1500(.20) + X (0.00) = (1500 + X).12

2) Do the math:

1500(.20) + X (0.00) = (1500 + X).12

300         =   180   +   .12X

120         =         .12X

3) Isolate for "X":

 120 = .12x .12 .12

4) Solution:

1000   =   X

You would need to add 1000ml of sterile water.

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