Proportion Pharmacy Math Question using 70% Dextrose and Tic-Tac-Toe Board

You need 50 mL of 5% dextrose for a patient. You have 70% dextrose 1000 mL on hand. How much concentrate will you need? How much diluent?

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5 parts 70% Dextrose (D5W) and 65 parts Sterile Water for Injection
by: David

Tic Tac Toe board:

higher strength
(top left):
.70%..........5 parts 70%
.....\....../............
..desired strength.......
.....(middle)............
........5%...............
...../.....\.............
.lower strength..........
....(bottom).............
0%............65 parts 0%
..........(sterile water)

The volume desired is 50ml of 5%.

Dividing 50ml into 70 equal parts:

50/70 = 5/7 = 0.714285

We will use 5 parts of the 70% dextrose.

5 X 0.7142 = (approx) 3.577mL

We will use 65 parts of the 0% solution.

(Sterile water for injection),

65 X 0.7142 = 46.423mL

In this example, the diluent (a substance used to dilute another substance) is the 65 parts of the 0% solution (46.423mL sterile water for injection.)

Also, in this example, the concentrate (or concentrated part of the volume) is the 70% dextrose (5 parts = 3.577mL)

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