The value of $y$ varies inversely as $\sqrt x$ and when $x=24$, $y=15$. What is $x$ when $y=3$?
This problem involves inverse variation, which means that $y=k/\sqrt x$ for some constant $k$. To find $k$, I can plug in the given values of $x$ and $y$: $15=k/\sqrt{24}$. Multiplying both sides by $\sqrt{24}$, I get $15\sqrt{24}=k$. Now I have an expression for $k$ in terms of $y$ and $\sqrt x$: $k=15\sqrt{24}=y\sqrt x$. I can use this expression to find $x$ when $y=3$: $15\sqrt{24}=3\sqrt x$. Dividing both sides by 3, I get $5\sqrt{24}=\sqrt x$. Squaring both sides, I get $25\cdot 24=x$. Simplifying, I get $x=600$. 