Answer:
206
Step-by-step explanation:
We have been given that Biologists tagged 103 fish in a lake January 1. On February 1, they returned and collected a random sample of 24 fish, 12 of which had been previously tagged.
To find the number of fish in the lake, we will use proportions because ratio of tagged fish and collected fish on February 1 will be equal to ratio of tagged fish and total fish on January 1.
[tex]\frac{\text{Tagged fish}}{\text{Collected fish}}=\frac{12}{24}[/tex]
Upon substituting the number of tagged fish in our proportion, we will get:
[tex]\frac{103}{\text{Total fish}}=\frac{12}{24}\\\\\frac{103}{\text{Total fish}}=\frac{1}{2}[/tex]
Cross multiply:
[tex]1\cdot \text{Total fish}=103\cdot 2\\\\\text{Total fish}=206[/tex]
Therefore, there are approximately 206 fishes in the lake.
