In this problem, the variables $x$, $y$, and $z$ are inversely proportional to the numbers 2, 3, and 5, respectively. Since they are inversely proportional, we can write:

$x \cdot 2 = y \cdot 3 = z \cdot 5 = k$

where $k$ is a constant. We will determine the values of $x$, $y$, and $z$ in terms of $k$, and then find the direct proportionality.

1. From $x \cdot 2 = k$, we get: $x = \frac{k}{2}$

2. From $y \cdot 3 = k$, we get: $y = \frac{k}{3}$

3. From $z \cdot 5 = k$, we get: $z = \frac{k}{5}$

To make $x$, $y$, and $z$ directly proportional, we express them in a form that matches the direct ratios. Let's set $k = 30$ (as it is a common multiple of 2, 3, and 5) to simplify calculations.

• $x = \frac{30}{2} = 15$
• $y = \frac{30}{3} = 10$
• $z = \frac{30}{5} = 6$

Thus, the values of $x$, $y$, and $z$ are directly proportional to 15, 10, and 6, respectively.

Answer

The correct answer is A) 15, 10, 6.

Would you like further details or have any questions?

Here are five related questions to expand on this topic:

1. How do we determine the constant of proportionality in inverse proportionality problems?
2. What are some common scenarios where direct and inverse proportions are used?
3. How would the answer change if the proportionality constants were different?
4. Can you give an example of a real-world application of inverse proportionality?
5. How does direct proportionality differ in equation form from inverse proportionality?

Tip: In problems with both direct and inverse proportions, finding a common multiple for constants simplifies calculations.