Question

A pharmacist is making a cough syrup from a concentrated solution that is 92% active ingredient. How much concentrate should be added to a 1-liter container of inactive ingredient to make a 12% solution of cough syrup? Round your answer to the nearest hundredth.

A. 0.23 liters

B. 0.44 liters

C. 0.57 liters

D. 0.68 liters

Answer 1

To make a 12% solution of cough syrup, approximately 0.13 liters of concentrate should be added to the 1-liter container of inactive ingredient.

Step-by-step explanation:

To make a 12% solution of cough syrup, we need to determine the amount of concentrate that should be added to the inactive ingredient. Let's assume the amount of concentrate needed is x liters.

The active ingredient in the concentrate is 92% of x liters (0.92x liters). The total volume of the solution is the sum of the active ingredient and the inactive ingredient, which is 1 liter.

Therefore, we have the equation: 0.92x + 0 liters = 0.12(1 liter).

Simplifying the equation gives us:

0.92x = 0.12

x = 0.12 / 0.92

x ≈ 0.1304

Rounding to the nearest hundredth gives us:

x ≈ 0.13 liters.

So, approximately 0.13 liters of concentrate should be added to the 1-liter container of inactive ingredient.