### Instruction: The numbers $x$ and $y$ are inversely proportional. When the sum of $x$ and $y$ is 42, $x$ is twice $y$. What is the value of $y$ when $x=-8$?### Response: Since $x$ and $y$ are inversely proportional, there must be some constant $k$ such that $xy=k$.
To find $k$, I can use the given information that $x+y=42$ and $x=2y$ when that happens.
Substituting $x=2y$ into $x+y=42$, I get $3y=42$, so $y=14$ and $x=28$.
Multiplying $x$ and $y$, I get $xy=28\cdot 14=392$, so $k=392$.
Now I can use this value of $k$ to find $y$ when $x=-8$.
Since $xy=k$, I can divide both sides by $x$ to get $y=\frac{k}{x}$.
Plugging in $x=-8$ and $k=392$, I get $y=\frac{392}{-8}=-49$.