1. **State the problem:** We are told that $y$ varies jointly with $x$ and $z$, and that $y=30$ when $x=5$ and $z=3$. We want to find the general formula for $y$ in terms of $x$ and $z$. 2. **Formula for joint variation:** When a variable $y$ varies jointly with $x$ and $z$, it means: $$y = kxz$$ where $k$ is the constant of proportionality. 3. **Find the constant $k$:** Use the given values $y=30$, $x=5$, and $z=3$: $$30 = k \times 5 \times 3$$ Simplify: $$30 = 15k$$ Divide both sides by 15: $$30 = \cancel{15}k \\ \frac{30}{\cancel{15}} = k \\ 2 = k$$ So, $k=2$. 4. **Write the general formula:** Substitute $k=2$ back into the formula: $$y = 2xz$$ **Final answer:** $$\boxed{y = 2xz}$$