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To solve this problem, let's first clarify the details:

- You have a 10-liter solution that is 90% acid.
- You want to mix it with pure water to create a mixture that is 90% water.

### Step-by-Step Solution:

1. **Identify the Acid and Water Content:**
   - The 10-liter solution is 90% acid, meaning it has 90% acid and 10% water.
   - In 10 liters, the amount of acid is \( 10 \times 0.9 = 9 \) liters.
   - The amount of water in the solution is \( 10 \times 0.1 = 1 \) liter.

2. **Define the Mixture:**
   - Let \( x \) be the amount of pure water (in liters) that you need to add.
   - After adding \( x \) liters of water, the total volume of the solution will be \( 10 + x \) liters.
   - The total water in the new solution will be \( 1 + x \) liters.

3. **Set Up the Equation:**
   - The problem states that the final mixture should be 90% water.
   - This means that the water content \( \frac{1 + x}{10 + x} \) should equal 90%, or 0.9.

   \[
   \frac{1 + x}{10 + x} = 0.9
   \]

4. **Solve the Equation:**
   - Multiply both sides by \( 10 + x \) to eliminate the fraction:

   \[
   1 + x = 0.9 \times (10 + x)
   \]

   - Distribute the 0.9 on the right side:

   \[
   1 + x = 9 + 0.9x
   \]

   - Subtract \( 0.9x \) from both sides:

   \[
   0.1x = 8
   \]

   - Solve for \( x \):

   \[
   x = \frac{8}{0.1} = 80 \text{ liters}
   \]

So, you should mix **80 liters** of pure water with the 10-liter solution to get a mixture that is 90% water.

Would you like more details on this process, or do you have any questions?

### Related Questions:
1. What would happen if the percentage of water in the initial solution was 20% instead of 10%?
2. How would the solution change if you wanted the final mixture to be 95% water instead of 90%?
3. Can you solve for the amount of water needed if the solution was only 5 liters instead of 10 liters?
4. What is the percentage of acid in the final solution after adding 80 liters of water?
5. How much water would you need to add to make the solution 50% water?

### Tip:
Always double-check your calculations by plugging the solution back into the original problem to ensure that all conditions are satisfied.

How many liters of pure water should be mixed with a 10-L solution of 90% acid to produce a mixture that is 90% water?

Solve a mixture problem where 90 liters of pure water are needed to mix with 10 liters of a 90% acid solution to produce a 90% water solution. This step-by-step guide includes key algebraic concepts and proportional reasoning, suitable for Grades 8-10.

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