Question

a pharmacist has 80 milliliters of a 25% saline solution. which expression can be used to find the percentage concentration of the final solution if she adds x milliliters of a 10% saline solution?
y = \frac{0.25(80)+0.1x}{x}cdot100
y = \frac{0.25(80)+0.1x}{80}cdot100
y = \frac{0.25(80)+0.1x}{80 + 0.1x}cdot100
y = \frac{0.25(80)+0.1x}{80 + x}cdot100

Explanation:

Step1: Calculate salt amount in each solution

The first solution has 80 milliliters with 25% salt - content, so the amount of salt is $0.25\times80$. The second solution has $x$ milliliters with 10% salt - content, so the amount of salt is $0.1x$.

Step2: Calculate total volume of final solution

The total volume of the final solution is the sum of the volumes of the two solutions, which is $80 + x$ milliliters.

Step3: Calculate percentage concentration of final solution

The percentage concentration $y$ of the final solution is the total amount of salt divided by the total volume of the solution, then multiplied by 100. So $y=\frac{0.25\times80 + 0.1x}{80 + x}\times100$.

Answer:

$y=\frac{0.25(80)+0.1x}{80 + x}\times100$ (corresponding to the fourth option in the original multiple - choice list)