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?
$y = \frac{0.25(80)+0.1x}{80+0.1x} \cdot 100$
$y = \frac{0.25(80)+0.1x}{x} \cdot 100$
$y = \frac{0.25(80)+0.1x}{80+x} \cdot 100$
$y = \frac{0.25(80)+0.1x}{80} \cdot 100$

Explanation:

Step1: Find amount of saline in each solution

The initial solution has 80 mL of 25% saline, so saline amount is \( 0.25(80) \). The added solution is \( x \) mL of 10% saline, so saline amount is \( 0.1x \). Total saline: \( 0.25(80) + 0.1x \).

Step2: Find total volume of final solution

Initial volume is 80 mL, added volume is \( x \) mL, so total volume: \( 80 + x \).

Step3: Calculate percentage concentration

Percentage concentration is (total saline / total volume) × 100. So \( y = \frac{0.25(80) + 0.1x}{80 + x} \cdot 100 \).

Answer:

\( y = \frac{0.25(80) + 0.1x}{80 + x} \cdot 100 \) (the third option in the original problem's display)