A bottle contains a mixture of 1 gram of powder and 4 milliliters of water. How many milliliters of water should be added to create a mixture with a powder-to-water ratio of 1:10?

To solve the problem, we need to determine how many milliliters of water should be added to the current mixture to achieve a powder-to-water ratio of 1:10.

### Step-by-Step Solution:

1. **Current Situation:**
   - Powder: 1 gram
   - Water: 4 milliliters

   The current powder-to-water ratio is \( \frac{1 \text{ gram}}{4 \text{ milliliters}} = \frac{1}{4} \).

2. **Desired Ratio:**
   - The goal is to have a powder-to-water ratio of 1:10, i.e., \( \frac{1 \text{ gram}}{10 \text{ milliliters}} \).

3. **Let \( x \) be the amount of water (in milliliters) to be added.**
   - After adding \( x \) milliliters of water, the total amount of water will be \( 4 + x \) milliliters.

4. **Set up the equation based on the desired ratio:**
   \[
   \frac{1 \text{ gram}}{4 + x \text{ milliliters}} = \frac{1}{10}
   \]

5. **Solve for \( x \):**
   \[
   1 \times (4 + x) = 10
   \]
   \[
   4 + x = 10
   \]
   \[
   x = 10 - 4 = 6
   \]

### Answer:
To achieve a powder-to-water ratio of 1:10, **6 milliliters of water** should be added.

Would you like any further details or explanations?

Here are 5 related questions to consider:
1. How would the solution change if the desired ratio was 1:5?
2. What if the initial amount of water was different, say 8 milliliters?
3. How does the powder-to-water ratio affect the concentration of the mixture?
4. If 3 grams of powder were used instead of 1 gram, what would the new amount of water required be?
5. How would the problem change if the total volume of the mixture had to stay constant?

**Tip:** When solving ratio problems, setting up an equation based on the desired ratio helps ensure accuracy in your calculations.

Learn how to adjust water volume in a mixture to achieve a powder-to-water ratio of 1:10. This problem involves basic ratio and proportion concepts, suitable for students in Grades 7-9.

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