An ointment contains 1% w/w calamine. What is the amount of calamine powder that should be added to 300 g of the ointment to produce a 5% w/w calamine ointment? (Note: Round the answer to 2 decimal places). 

Choose the best answer

10.82 g

12.63 g

13.54 g

14.32 g

To solve this problem, we need to determine how much calamine powder should be added to 300 g of a 1% w/w calamine ointment to increase the concentration to 5% w/w.

### Step-by-Step Solution:

1. **Determine the amount of calamine in the original 300 g of 1% ointment:**
   - Since the ointment contains 1% calamine by weight, the amount of calamine already present in the 300 g is:
   \[
   \text{Amount of calamine} = \frac{1}{100} \times 300 = 3 \text{ g}
   \]

2. **Let \( x \) be the amount of calamine powder to be added.**
   - After adding \( x \) grams of calamine powder, the total weight of the ointment becomes \( 300 + x \) grams, and the total amount of calamine will be \( 3 + x \) grams.

3. **Set up the equation for the final concentration:**
   - We want the final ointment to have 5% w/w calamine, which means:
   \[
   \frac{3 + x}{300 + x} = \frac{5}{100} = 0.05
   \]

4. **Solve for \( x \):**
   - Multiply both sides by \( 300 + x \):
   \[
   3 + x = 0.05(300 + x)
   \]
   - Expand the right side:
   \[
   3 + x = 15 + 0.05x
   \]
   - Collect like terms:
   \[
   x - 0.05x = 15 - 3
   \]
   \[
   0.95x = 12
   \]
   - Solve for \( x \):
   \[
   x = \frac{12}{0.95} = 12.63 \text{ g}
   \]

Thus, the amount of calamine powder that should be added is **12.63 g**.

### Final Answer:
**12.63 g**

Do you want more details or have any questions?

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Here are 5 related questions:
1. How would the calculation change if the final concentration was 10% w/w?
2. What is the meaning of w/w concentration in pharmaceuticals?
3. How would you calculate the amount of base ointment to dilute a higher concentration ointment to a lower concentration?
4. What is the amount of calamine in a 500 g ointment with 3% w/w concentration?
5. How can you adjust the concentration of an ointment when the required amount of active ingredient is limited?

**Tip:** When working with percentages, always ensure consistency in units (e.g., weight/weight for w/w).

An ointment contains 1% w/w calamine. What is the amount of calamine powder that should be added to 300 g of the ointment to produce a 5% w/w calamine ointment? (Note: Round the answer to 2 decimal places).

Find out how to calculate the amount of calamine powder needed to increase the concentration from 1% to 5% in a 300 g ointment. This problem involves key algebraic concepts and percentage calculations. Perfect for students in Grades 9-12.

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