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The image shows a series of math problems, including questions about interval notation, alcohol solution mixing, and coffee blend pricing.

For **Question 4** (regarding the alcohol solution):
- You are asked to mix a 25% alcohol solution. You have 175 mL of a 75% alcohol solution on hand and need to determine how much pure water you should add to obtain the 25% solution.

### Solving:
1. Let \( x \) represent the amount of pure water (0% alcohol) you need to add.
2. The total amount of alcohol from the 75% solution is \( 0.75 \times 175 \) mL.
3. After adding \( x \) mL of pure water, the total volume will be \( 175 + x \) mL.
4. To achieve a 25% alcohol solution, the total alcohol content must be \( 0.25 \times (175 + x) \).

#### Equation setup:
\[
0.75 \times 175 = 0.25 \times (175 + x)
\]
Solving this will give you the amount of water to add.

#### Solving the equation:
\[
131.25 = 0.25 \times (175 + x)
\]
\[
131.25 = 43.75 + 0.25x
\]
\[
131.25 - 43.75 = 0.25x
\]
\[
87.5 = 0.25x
\]
\[
x = \frac{87.5}{0.25} = 350
\]

Thus, you need to add **350 mL of pure water**.

Would you like more details or further explanations? Here are a few related questions to deepen your understanding:

1. How would the equation change if you started with a different percentage of alcohol?
2. What if you wanted to create a solution with a different target percentage (e.g., 40%)?
3. Can you generalize the formula for mixing any two solutions with different concentrations?
4. How would this change if the solution contained a substance other than alcohol?
5. What are the practical applications of this type of problem in everyday life?

### Tip:
In mixture problems, always track the total amount of the substance of interest (in this case, alcohol) and ensure that the equation accounts for both the quantity and the concentration of the solution.

You need a 25% alcohol solution. On hand, you have a 175 mL of a 75% alcohol mixture. How much pure water will you need to add to obtain the desired solution?

Learn how to solve a solution mixture problem where you calculate how much pure water is needed to dilute a 75% alcohol solution to a 25% concentration. This detailed step-by-step guide uses algebraic equations and mixture concepts, ideal for high school students.

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