The variable y varies inversely with x. When x=4, y=15. What is the value of y when x=20?

Inverse variation means the product $xy$ stays constant. From $x = 4$ and $y = 15$, $k = 60$. When $x = 20$, $y = \frac{60}{20} = 3$. Check: $x$ grew by a factor of 5, so $y$ should shrink by a factor of 5, and $15 \div 5 = 3$. A common wrong answer is 75, which treats the relationship as direct variation and multiplies by 5. Another is 31, from adding the increase in $x$ (16) to $y$. Another is 11, from subtracting 4 from 15. When $x$ grows, $y$ shrinks in proportion, so divide a fixed product.