You need a 45% alcohol solution. On hand, you have a 225 mL of a 85% alcohol mixture. How much pure water will you need to add to obtain the desired solution?

Question

You need a 45% alcohol solution. On hand, you have a 225 mL of a 85% alcohol mixture. How much pure water will you need to add to obtain the desired solution?

A) Write an equation using the information as it is given above that can be used to solve this problem. Use
X as your variable to represent the amount of pure water you need to use.
Equation:

Answer 1

0.85(225) = 0.45(225+X)

Answer 2

Let X represent the amount of pure water needed to be added.

The total volume of the final solution will be 225 mL + X mL.

Since the alcohol concentration in the 85% alcohol mixture is 85%, we can write the equation:

225 mL × 85% + X mL × 0% = (225 mL + X mL) × 45%

This equation represents the conservation of alcohol in the solution. The left side of the equation represents the amount of alcohol in the initial 85% alcohol mixture, and the right side represents the amount of alcohol in the final 45% alcohol solution after adding X mL of pure water.