Question

A pharmacist wants to mix a 45% saline solution with a 27% saline solution to get 108 mL of a 40% saline solution. How much of each solution should she use? Round your answer to the nearest mL.

Answer 1

To create 108 mL of a 40% saline solution, the pharmacist needs to mix 78 mL of 45% saline solution with 30 mL of 27% saline solution.

Step-by-step explanation:

To solve this problem, we will use the concept of a mixture, which is a common topic in algebra.

Since we want to mix two solutions of different concentrations to obtain a final solution with a specific volume and concentration, we can set up an equation to represent the concentrations of the individual solutions and how they contribute to the final mixture.

Let's define the amount of the 45% saline solution as x milliliters and the amount of the 27% saline solution as y milliliters.

Step 1: Set up the equations

The first equation represents the total final volume of the solution:

x + y = 108 mL

The second equation comes from the total amount of saline in the mixture:

0.45x + 0.27y = 0.40(108)

Step 2: Solve for one variable

We can solve the first equation for y:

y = 108 - x

Now substitute y into the second equation:

0.45x + 0.27(108 - x) = 43.2

Step 3: Simplify and solve for x

0.45x + 29.16 - 0.27x = 43.2

0.18x = 43.2 - 29.16

0.18x = 14.04

x = 78 mL (approximately)

Using x in the first equation:

y = 108 - 78

y = 30 mL

The pharmacist should use 78 mL of the 45% saline solution and 30 mL of the 27% saline solution to make 108 mL of a 40% solution, when rounding to the nearest mL.