1. **State the problem:** We know that $x$ is inversely proportional to $y$. Given $y=27$ when $x=14$, find $x$ when $y=21$. 2. **Formula and rule:** If $x$ is inversely proportional to $y$, then $x = \frac{k}{y}$ for some constant $k$. 3. **Find the constant $k$:** Using the given values, $$14 = \frac{k}{27} \implies k = 14 \times 27 = 378$$ 4. **Find $x$ when $y=21$:** Substitute $k=378$ and $y=21$ into the formula, $$x = \frac{378}{21} = 18$$ 5. **Answer:** The value of $x$ when $y=21$ is $18$.