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To solve this problem, we need to determine how many deals each employee closed based on the given clues and then adjust the pie chart to match the correct percentages.

### Information Given:
1. The total number of deals closed by all employees is **40**.
2. **Adam** closed **10 deals**.
3. **Charles** closed **1/3 more deals than Barbara**.
4. **Daniela** closed **twice as many deals as Charles**.

### Step-by-Step Solution:
1. Let:
   - The number of deals closed by Barbara be \( B \).
   - Then, Charles closed \( B + \frac{1}{3}B = \frac{4}{3}B \) deals.
   - Daniela closed \( 2 \times \frac{4}{3}B = \frac{8}{3}B \) deals.

2. Now we know the total number of deals closed:
   \[
   10 + B + \frac{4}{3}B + \frac{8}{3}B = 40
   \]

3. Combine terms:
   - Convert \( B \), \( \frac{4}{3}B \), and \( \frac{8}{3}B \) to a common fraction.
   - This gives:
     \[
     10 + B + \frac{4B}{3} + \frac{8B}{3} = 40
     \]

4. Simplify the equation:
   - Combine \( B \) terms: \( B + \frac{4B}{3} + \frac{8B}{3} = \frac{3B + 4B + 8B}{3} = \frac{15B}{3} = 5B \).
   - So, \( 10 + 5B = 40 \).

5. Solve for \( B \):
   \[
   5B = 30 \Rightarrow B = 6
   \]

6. Now substitute \( B = 6 \) back to find the deals for each employee:
   - **Barbara**: \( B = 6 \).
   - **Charles**: \( \frac{4}{3}B = \frac{4}{3} \times 6 = 8 \).
   - **Daniela**: \( \frac{8}{3}B = \frac{8}{3} \times 6 = 16 \).

7. Summary of deals closed:
   - **Adam**: 10 deals
   - **Barbara**: 6 deals
   - **Charles**: 8 deals
   - **Daniela**: 16 deals

8. **Verification**:
   - Total = \( 10 + 6 + 8 + 16 = 40 \), which matches the given total.

### Adjust the Pie Chart:
Now, calculate the percentage of total deals each person closed:
- **Adam**: \( \frac{10}{40} \times 100 = 25\% \)
- **Barbara**: \( \frac{6}{40} \times 100 = 15\% \)
- **Charles**: \( \frac{8}{40} \times 100 = 20\% \)
- **Daniela**: \( \frac{16}{40} \times 100 = 40\% \)

### Final Answer for the Pie Chart:
- **Adam**: 25%
- **Barbara**: 15%
- **Charles**: 20%
- **Daniela**: 40%

Would you like further details or clarification?

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**Related Questions**:
1. How would the solution change if Daniela closed three times as many deals as Charles?
2. What if the total deals were 50 instead of 40?
3. How can you verify pie chart data when the total is not given?
4. What if Barbara closed twice the number of deals instead of one-third less?
5. How would you adjust percentages if Charles closed 5 more deals than Barbara?

**Tip**: When solving percentage problems, always verify by summing percentages to check that they match 100%.

Four employees at a company closed 40 deals this week. Adam closed 10 deals. Charles closed 1/3 more deals than Barbara. Daniela closed twice as many deals as Charles. Adjust the pie chart to represent this week's sales.

Learn how to calculate the distribution of sales deals closed by four employees, given specific conditions. This problem covers algebraic methods, ratios, and percentages. Perfect for students in Grades 9-11.

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