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The given equation is:

\[
x \% \text{ of } 475 + 24\% \text{ of } 650 = 346
\]

This can be rewritten in mathematical terms as:

\[
\frac{x}{100} \times 475 + \frac{24}{100} \times 650 = 346
\]

Let's solve this equation step by step.

1. Calculate \(24\% \) of 650:
   \[
   \frac{24}{100} \times 650 = 156
   \]
   
   Now the equation becomes:
   \[
   \frac{x}{100} \times 475 + 156 = 346
   \]

2. Subtract 156 from both sides:
   \[
   \frac{x}{100} \times 475 = 346 - 156
   \]
   \[
   \frac{x}{100} \times 475 = 190
   \]

3. Multiply both sides by 100 and divide by 475:
   \[
   x = \frac{190 \times 100}{475}
   \]
   
   Let me calculate that.The value of \( x \) is 40.

So, the solution to the equation is \( x = 40 \).

Would you like more details or have any questions about this process? Here are five related questions to deepen your understanding:

1. How can you generalize the method used to solve this percentage problem for different numbers?
2. How would the solution change if the percentage values were different, say 30% of 475 and 20% of 650?
3. Can you express \( x \% \) of a number as a fraction instead of using percentages?
4. What is the significance of isolating \( x \) in this type of algebraic equation?
5. How can this method be applied to word problems involving percentages?

**Tip:** When solving percentage problems, always convert percentages to their decimal form (e.g., 40% becomes 0.40) for easier manipulation in equations.

Learn how to solve the equation involving percentages and linear equations: x % of 475 + 24% of 650 = 346. This problem covers key mathematical concepts such as percentage calculation and linear equations, providing a detailed step-by-step solution suitable for students in Grades 7-10.

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