2023 AMC 8 Problem 5

A lake contains 250 trout, along with a variety of other fish. When a marine biologist catches and releases a sample of 180 fish from the lake, 30 are identified as trout. Assume that the ratio of trout to the total number of fish is the same in both the sample and the lake. How many fish are there in the lake?

\textbf{(A)} 1250 \qquad \textbf{(B)} 1500 \qquad \textbf{(C)} 1750 \qquad \textbf{(D)} 1800 \qquad \textbf{(E)} 2000

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.