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:

$\frac{5}{75}=\frac{250}{x}$

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

$\begin{gathered} x(\frac{5}{75})=250 \\ x=250(\frac{75}{5}) \\ x=3750 \end{gathered}$

Hence, there are 3750 fishes

b) The same as before:

$\begin{gathered} \frac{250}{5500}=\frac{15}{x} \\ x(\frac{250}{5500})=15 \\ x=15(\frac{5500}{250}) \\ x=330 \end{gathered}$

Hence, there are a total number of 330 fishes