Since $y$ varies directly as $x$ and inversely as $z$, we can express the relationship as:

$y = k \frac{x}{z}$

where $k$ is the constant of proportionality.

Step 1: Find $k$ using the given values

We're given:

• $y = 36$
• $x = 10$
• $z = 5$

Plugging these values into the equation:

$36 = k \frac{10}{5}$

Simplify the fraction:

$36 = k \cdot 2$

Now, solve for $k$:

$k = \frac{36}{2} = 18$

So, $k = 18$.

Step 2: Find $y$ when $x = 3$ and $z = 15$

Now we use the equation with the new values for $x$ and $z$:

$y = 18 \frac{3}{15}$

Simplify $\frac{3}{15}$ to $\frac{1}{5}$:

$y = 18 \cdot \frac{1}{5} = \frac{18}{5} = 3.6$

Answer

When $x = 3$ and $z = 15$, $y = 3.6$.

Would you like further clarification on any part?

Related Questions

1. What would $y$ be if $x = 6$ and $z = 10$?
2. How would $y$ change if $z$ were doubled, keeping $x$ constant?
3. What if $y$ varies directly as $x$ and directly as $z$ as well?
4. How would the solution change if $y$ were inversely proportional to both $x$ and $z$?
5. If $y$ varies directly as $x$ squared, how would that affect the formula?

Tip:

For direct and inverse variations, always isolate the constant $k$ first using initial conditions; then apply it to find unknown values.