Question

a biologist tagged 250 fish then collected another sample of 75 fish, of which 5 were tagged. How many fish would she estimate are in the lake.a biologist estimated that there were 5500 fish in a lake in which 250 fish have been tagged. a ranger collected a sample in which there were 15 tagged fish approximately how many fish were in the sample the ranger collected ?

Answer 1

a) You take into account that for 75 fish there are 5 tagged. If it is necessary that the proportion is equal, for 250 tagged fish you have a sample of x fishes.

To find the total number of fishes you write the following equation:

`(5)/(75)=(250)/(x)`

where x is the unknown number of total fishes with 250 tagged fishes. You solve the previous equation for x:

`\begin{gathered} x((5)/(75))=250 \\ x=250((75)/(5)) \\ x=3750 \end{gathered}`

Hence, there are 3750 fishes

b) The same as before:

`\begin{gathered} (250)/(5500)=(15)/(x) \\ x((250)/(5500))=15 \\ x=15((5500)/(250)) \\ x=330 \end{gathered}`

Hence, there are a total number of 330 fishes