Let's solve the equation:

\[
20y + 38y + 92 = 36y + 600
\]

### Step 1: Combine like terms on both sides of the equation.

On the left side:

\[
20y + 38y = 58y
\]

So the equation becomes:

\[
58y + 92 = 36y + 600
\]

### Step 2: Move the variable terms to one side and constants to the other.

Subtract \(36y\) from both sides:

\[
58y - 36y + 92 = 600
\]

This simplifies to:

\[
22y + 92 = 600
\]

### Step 3: Subtract 92 from both sides to isolate the term with \(y\).

\[
22y = 600 - 92
\]

\[
22y = 508
\]

### Step 4: Divide by 22 to solve for \(y\).

\[
y = \frac{508}{22} = 23.09
\]

### Final answer:
\[
y \approx 23.09
\]

Would you like more details or have any questions?

Here are 5 related questions to extend your understanding:
1. How would you solve an equation if it contained fractions?
2. Can you solve equations with multiple variables?
3. What happens if the equation has no solution or infinite solutions?
4. How do we check if a solution is correct?
5. Can you apply this process to a quadratic equation?

**Tip**: Always check your solution by plugging it back into the original equation to verify if both sides are equal.

Learn how to solve the linear equation 20y + 38y + 92 = 36y + 600 with a detailed step-by-step solution. This problem introduces key algebraic concepts, including combining like terms and isolating variables, making it suitable for students in Grades 8-10.

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