Massachusetts Pharmacy Technician License Practice Test

If a prescription for 180 g of a 7.5% ointment is to be prepared, which formula could be used with 10% and 2% strengths?

1. 120 g of 10% + 60 g of 2%

2. 150 g of 10% + 30 g of 2%

3. 123.75 g of 10% + 56.25 g of 2%

4. 90 g of 10% + 90 g of 2%

The correct answer is: 123.75 g of 10% + 56.25 g of 2%

To determine the correct formula for preparing 180 g of a 7.5% ointment using the available strengths of 10% and 2%, it is essential to consider the concept of alligation, which is a method used to mix solutions of different concentrations to achieve a desired concentration. The desired concentration is 7.5%, while you have one ointment at 10% and another at 2%. To find out how much of each concentration is needed, you can set up equations based on the mixture. When calculating the total amount of the mixture, you need to account for both the total weight and the weight contributed by each component to the final concentration. For example, the 10% solution contributes more active ingredient per gram than the 2% solution, and this difference is critical when calculating the proportions needed. In this case, the formula that works out to yield 180 g of a 7.5% ointment is achieved by using 123.75 g of the 10% solution and 56.25 g of the 2% solution. This combination effectively balances the higher concentration with enough of the lower concentration to average out to the target percentage. In this particular mix, the calculation for the total weight