The equation provided is:

$\frac{2}{3} \text{ of } y = \frac{8}{15} \text{ of } z$

This can be rewritten as:

$\frac{2}{3} \times y = \frac{8}{15} \times z$

Now, let's isolate $\frac{y}{z}$ to find the ratio $y : z$.

Step 1: Set up the equation

$\frac{2}{3} \times y = \frac{8}{15} \times z$

Step 2: Divide both sides by $z$ and multiply both sides by 15 to eliminate the denominator on the right side:

$15 \times \left( \frac{2}{3} \times y \right) = 8 \times z$

This simplifies to: $10y = 8z$

Step 3: Solve for $\frac{y}{z}$

$\frac{y}{z} = \frac{8}{10} = \frac{4}{5}$

Thus, the ratio $y : z$ is $5:4$.

Would you like further details or have any questions? Here are 5 related questions to expand your understanding:

1. How do you solve problems involving ratios and proportions in different contexts?
2. What happens to a ratio if one of the values is doubled?
3. How can you apply this concept of ratios to problems involving scaling?
4. How do ratios differ from fractions in mathematical operations?
5. Can this method be used to solve more complex equations involving percentages?

Tip: Always simplify ratios to their lowest terms for clarity.