AMC8 2023

AMC8 2023 · Q5

AMC8 2023 · Q5. It mainly tests Ratios & proportions.

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?

一个湖中有 $250$ 条鳟鱼，还有各种其他鱼类。当海洋生物学家从湖中捕获并放回 $180$ 条鱼的样本时，其中 $30$ 条被识别为鳟鱼。假设样本与湖中鳟鱼与总鱼类的比例相同。湖中有多少条鱼？

(A) \ 1250 \ 1250

(B) \ 1500 \ 1500

(D) \ 1800 \ 1800

(E) \ 2000 \ 2000

Answer

Correct choice: (B)

正确答案：（B）

Solution

Note that \[\frac{\text{number of trout}}{\text{total number of fish}} = \frac{30}{180} = \frac16.\] So, the total number of fish is $6$ times the number of trout. Since the lake contains $250$ trout, there are $250\cdot6=\boxed{\textbf{(B)}\ 1500}$ fish in the lake.

注意 \[\frac{\text{鳟鱼数量}}{\text{总鱼类数量}} = \frac{30}{180} = \frac16.\] 所以，总鱼类数量是鳟鱼数量的 $6$ 倍。由于湖中有 $250$ 条鳟鱼，因此湖中总共有 $250\cdot6=\boxed{\textbf{(B)}\ 1500}$ 条鱼。

Topics

AR.004 Ratios & proportions