The variable y varies inversely with x. When x=4, y=5. What is the value of y when x=10?

In inverse variation, the product $xy$ stays constant. From $x = 4$ and $y = 5$, the constant is $k = 20$. When $x = 10$, $y = \frac{20}{10} = 2$, choice B. Choice A (2.5) comes from halving 5, which would be right if $x$ doubled to 8. Choice C (12.5) comes from multiplying by $\frac{10}{4}$, treating the relationship as direct variation. Choice D (0.5) comes from computing $\frac{5}{10}$, dividing by $x$ without using the constant. For inverse variation, when $x$ is multiplied by 2.5, $y$ is divided by 2.5.