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.