To solve the equation:

\[
5 = \frac{100}{y \cdot (2 + 3)}
\]

### Step-by-step solution:

1. Simplify the expression inside the parentheses:
   \[
   5 = \frac{100}{y \cdot 5}
   \]

2. Now, multiply the \( y \) by 5 in the denominator:
   \[
   5 = \frac{100}{5y}
   \]

3. Multiply both sides of the equation by \( 5y \) to eliminate the denominator:
   \[
   5(5y) = 100
   \]

   Simplifying:
   \[
   25y = 100
   \]

4. Solve for \( y \) by dividing both sides by 25:
   \[
   y = \frac{100}{25} = 4
   \]

### Final answer:
\[
y = 4
\]

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. What if the original equation was \( 10 = \frac{100}{y \cdot (2 + 3)} \)?
2. How would the solution change if the equation had a different numerator, say \( \frac{150}{y \cdot (2 + 3)} \)?
3. How can you verify the solution by substituting \( y = 4 \) back into the equation?
4. What is the impact of changing the value inside the parentheses (e.g., \( 2 + 4 \) instead of \( 2 + 3 \))?
5. How can this approach be generalized to solve other fractional equations?

**Tip:** Always simplify expressions inside parentheses first to make solving easier!

Learn how to solve the linear equation 5 = 100 / y * (2 + 3) with a detailed step-by-step solution. This problem covers core algebraic concepts like simplifying fractions and solving for unknowns, suitable for students in Grades 6-8.

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