Question

a prescription calls for 75 ml of 75% alcohol; however, the pharmacy only has 95% alcohol and sterile water. which of the following is the amount of 95% alcohol and sterile water needed? choose an answer 1 59 ml of 95% alcohol and 16 ml of sterile water 2 45 ml of 95% alcohol and 30 ml of sterile water 3 65 ml of 95% alcohol and 10 ml of sterile water 4 70 ml of 95% alcohol and 5 ml of sterile water

Explanation:

Step1: Set up alcohol - amount equation

Let $x$ be the volume of 95% alcohol. The amount of pure alcohol in 95% alcohol is $0.95x$. The final volume is 75 mL of 75% alcohol, so the amount of pure alcohol in the final solution is $0.75\times75$.

Step2: Solve for $x$

We have the equation $0.95x=0.75\times75$. Then $x = \frac{0.75\times75}{0.95}=\frac{56.25}{0.95}\approx59$ mL.

Step3: Calculate volume of sterile water

The volume of sterile water $y=75 - x$. Substituting $x\approx59$ mL, we get $y = 75 - 59=16$ mL.

Answer:

1. 59 mL of 95% alcohol and 16 mL of sterile water