Question

A pharmacist wants to mix a 39% saline solution with a 12% saline solution to get 96 ml of a 30% saline solution. How much of each solution should be used? (Round your answer to the nearest ml)

A) 72 ml of 39% solution and 24 ml of 12% solution
B) 60 ml of 39% solution and 36 ml of 12% solution
C) 48 ml of 39% solution and 48 ml of 12% solution
D) 36 ml of 39% solution and 60 ml of 12% solution

Answer 1

The pharmacist should use approximately 64 ml of the 39% saline solution and 32 ml of the 12% saline solution to obtain 96 ml of a 30% saline solution.

Step-by-step explanation:

To find out how much of each saline solution the pharmacist should use to get 96 ml of a 30% saline solution, we can set up a system of equations. Let x be the volume of the 39% solution and y be the volume of the 12% solution. We have:

• x + y = 96 (The total volume of the final solution must be 96 ml)
• 0.39x + 0.12y = 0.30(96) (The total amount of saline in the final solution)

From the second equation, we get, 0.39x + 0.12y = 28.8. We can solve this system of equations either by substitution or the elimination method. Using elimination:

• Multiply the first equation by -0.12: -0.12x - 0.12y = -11.52
• Add this to the second equation: (0.39x - 0.12x) + (0.12y - 0.12y) = 28.8 - 11.52
• Simplify to find x: 0.27x = 17.28
• Divide by 0.27 to solve for x: x ≈ 64 ml (Rounded to nearest ml)
• Using x + y = 96, find y: 64 + y = 96 => y = 96 - 64 => y ≈ 32 ml (Rounded to nearest ml)

Thus, the pharmacist should use approximately 64 ml of the 39% saline solution and approximately 32 ml of the 12% saline solution. This is closest to option A provided by the student. It is important to understand that while we are using approximate values due to rounding, the real answer might be very close to the calculated figures but not exactly the same due to rounding.