Answer
The total number of trout is 287 in a lake.
Work Step by Step
Let, the total number of trout is \[x\], catches 112 trout are tagged as \[\frac{x}{112}\]. And, later 82 trout are caught and 32 of them are \[\frac{82}{32}\].
Therefore, two proportions of the total to tagged trout: total/tagged.
Just set these two equal and solve for \[x\].
\[\frac{x}{112}=\frac{82}{32}\]
i.e.,
\[\begin{align}
& x=\frac{82}{32}\times 112 \\
& =287
\end{align}\]
Thus, the total number of trout is 287 in a lake.
