Question

A pharmacist mixes 14 ounces of 68% saline solution with 55% saline solution. If the final mixture is 62% saline, how many ounces of the 55% solution were used?

Answer 1

The student's question involves using a weighted average to find the amount of a 55% saline solution needed when mixed with a 14-ounce 68% saline solution to make a final mixture that is 62% saline.

Step-by-step explanation:

The student is asking how to determine the amount of a 55% saline solution needed when it is mixed with a 14-ounce 68% saline solution to achieve a final mixture that is 62% saline. This is a mathematical problem that involves using the concept of weighted averages.

Let x be the number of ounces of the 55% saline solution. The total amount of saline in the 68% solution is 0.68 times 14 ounces and the amount of saline in the 55% solution is 0.55 times x ounces. The final mixture, which is x + 14 ounces, should be a 62% saline solution.

To solve for x, we set up the equation:
0.68 × 14 + 0.55 × x = 0.62 × (14 + x)

Upon solving this equation, we can find the value of x, which represents the amount of the 55% solution added.