A biologist wants to estimate the number of fish living in a lake. She caught 106 fish, tagged each one, and then released them back into the lake. After a few days, she caught 227 fish, and found that 11 of them were tagged. Use a proportion to estimate the number of fish living in this lake.
total number ---- x
106/x = 11/227
11x = 240062
x = 2187.45..
there are appr 2187 fish in the lake
Well, well, well, it seems like the biologist has been quite the fish catcher! Let's dive into this fishy situation, shall we?
If the biologist caught 106 fish, tagged them all, and released them back into the lake, we can assume that these tagged fish are now buzzing around with their untagged friends.
After a few days, the biologist caught 227 fish, and found that 11 of them were tagged. Now, we're going to use some mathematical clown magic and set up a proportion to estimate the total number of fish in the lake.
If 11 tagged fish were caught out of 227 fish, we can write it like this:
11/227 = 106/x
Now, let's cross-multiply:
11x = 227 * 106
Oh, oh, don't worry, I'll use my calculator for this one! *Beep boop beep* Okay, so we have:
11x = 24,082
And now, let's bring the x, the very elusive number of fish, out from hiding:
x = 24,082 / 11
Aha! We now have our answer! According to my clown calculations, there are approximately 2,189.273 fish living in this lake.
But, remember, this is just an estimate, and fish have quite a knack for playing hide-and-seek, so take it with a pinch of saltwater!
Hope that brings a splash of amusement to your day!
To estimate the number of fish living in the lake, we'll create a proportion using the tagged fish as a sample.
Let's denote the number of fish in the lake as "x".
We know that the proportion of tagged fish in the sample is equal to the proportion of tagged fish in the entire population.
The proportion can be expressed as:
Number of tagged fish in sample / Number of fish in sample = Number of tagged fish in population / Number of fish in population
We can substitute the known values we have:
11 fish tagged in the sample / 227 fish in the sample = 106 fish tagged in the population / x fish in the population
Now, we can solve for x.
(11 / 227) = (106 / x)
To isolate x, we will cross-multiply:
11x = 227 * 106
Now calculate:
11x = 24,062
Divide both sides by 11 to solve for x:
x = 24,062 / 11
x ≈ 2187
Based on this estimation, there are approximately 2,187 fish living in the lake.
To estimate the number of fish living in the lake using a proportion, we can set up a ratio between the number of tagged fish and the total population of fish.
Let's denote the total population of fish in the lake as "x".
According to the given information, the biologist caught 106 fish and tagged each one. Then, after a few days, she caught a total of 227 fish, out of which 11 were tagged.
We can set up a proportion using this information:
(tagged fish)/(total fish) = (tagged fish caught)/(total fish caught)
Plugging in the values, we get:
11/x = 106/227
To solve for x, we can cross-multiply:
11 * 227 = 106 * x
2517 = 106 * x
Dividing both sides by 106:
x = 2517/106
x ≈ 23.72
Therefore, the estimated number of fish living in the lake is approximately 23.72.