Biologists tagged 180 fish in a lake on January 1. On February 1, they returned and collected a random sample of 4545 fish, 1515 of which had been previously tagged. On the basis of this experiment, approximately how many fish does the lake have?
Assuming typos, 1/3 of the fish found in February were tagged.
So, 180 represents 1/3 of the fish in the lake.
To estimate the total number of fish in the lake, we can use the concept of ratio.
This problem can be solved using a proportion:
Let's assume the total number of fish in the lake is 'x'.
According to the information given:
- 180 fish were tagged initially.
- On February 1, a sample of 4545 fish was collected, out of which 1515 were tagged.
So, we can set up the following proportion:
(Initial tagged fish)/(Initial total fish) = (Sample tagged fish)/(Sample total fish)
In this case:
180/x = 1515/4545
To solve this proportion, we can cross-multiply and solve for 'x':
180 * 4545 = 1515 * x
817,350 = 1515x
Divide both sides of the equation by 1515 to solve for 'x':
x = 817,350 / 1515
After performing the calculation, we find that the estimated total number of fish in the lake is approximately 539.80. Since we cannot have a fraction of a fish, we should round this down to the nearest whole number.
Therefore, approximately, the lake has 539 fish.