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The problem provided is as follows:

A company divided a bonus among its employees **A**, **B**, and **C** in the ratio 2:3:7. **C's** bonus was **X%** more than the combined bonus of **A** and **B**. We are asked to find the value of **X**.

### Step-by-step solution:

1. **Let the total amount of the bonus be** $ k $. The bonuses for **A**, **B**, and **C** are given in the ratio of 2:3:7. So, let:
   - A's bonus = $ 2k $
   - B's bonus = $ 3k $
   - C's bonus = $ 7k $

2. **The combined bonus of A and B** is:
   \[
   2k + 3k = 5k
   \]

3. **C's bonus** is given as **X% more than the combined bonus of A and B**. This can be expressed as:
   \[
   7k = 5k + \frac{X}{100} \times 5k
   \]

4. **Simplify the equation**:
   \[
   7k = 5k \left(1 + \frac{X}{100}\right)
   \]
   Divide both sides by $ 5k $:
   \[
   \frac{7}{5} = 1 + \frac{X}{100}
   \]

5. **Solve for X**:
   \[
   \frac{7}{5} - 1 = \frac{X}{100}
   \]
   \[
   \frac{2}{5} = \frac{X}{100}
   \]
   Multiply both sides by 100:
   \[
   X = \frac{2}{5} \times 100 = 40
   \]

So, **X = 40**.

Would you like further clarification or details on any part of the solution?

Here are 5 related questions for further practice:
1. If the total bonus is $10,000, how much does each employee receive?
2. What would happen if the ratio of the bonuses was 3:5:8 instead of 2:3:7?
3. How would the result change if C's bonus was X% less than the combined bonuses of A and B?
4. If the total bonus distribution changes such that the combined bonus of A and B is twice that of C, what would be the new ratio?
5. Can you express the combined bonuses of A and B as a percentage of the total bonus?

**Tip:** When solving percentage problems, breaking the relationship into algebraic equations often simplifies the process and makes the solution more apparent.

A company divided a bonus among its employees A, B, and C in the ratio 2:3:7. C's bonus was X% more than the combined bonus of A and B. Find X.

Learn how to solve a problem involving the distribution of a bonus among three employees in the ratio 2:3:7, where C's bonus is X% more than the combined bonuses of A and B. This step-by-step solution covers concepts like ratios, percentages, and algebra. Suitable for students in Grades 9-11.

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