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!