The variable y varies inversely with x. When x=6, y=8. What is the value of y when x=16?

Inverse variation means $xy$ is constant. From $x = 6$ and $y = 8$, the constant is $k = 48$. When $x = 16$, $y = \frac{48}{16} = 3$. Check: $x$ is multiplied by $\frac{16}{6} = \frac{8}{3}$, so $y$ must be divided by $\frac{8}{3}$, which is $8 \times \frac{3}{8} = 3$. A common wrong answer is 21.3, which results from treating the relationship as direct variation, $8 \times \frac{16}{6}$. Another is 18, from adding the change in $x$ (10) to $y$ with a slip. Inverse variation divides a fixed product, and when one variable grows the other shrinks.