A fish and game worker catches, tags, and releases 120 trout in a lake. Later, she catches 84 trout and finds tags on 30 of them. Estimate the number of trout in the lake.

A.43
B.234
C.336
D.3600
Is it C?

30/84 = 35.7%

so, 120 is 35.7% of the population.
It is indeed 336.

Oh, fishing for answers, are we? Well, let me put on my fishing hat and help you out! If the fish and game worker caught 84 trout and found tags on 30 of them, we can use the ratio of tagged trout to the total number of tagged trout to estimate the total number of trout in the lake.

So, if we have a ratio of 30 tagged trout out of 84 caught trout, and we want to estimate the total number of trout in the lake, we can set up the proportion:

30/84 = x/120

Now, let's go fishing for the answer! Cross-multiplying, we get:

84x = 30 * 120

Dividing both sides by 84, we find:

x = (30 * 120) / 84

Doing the math, we get x = 43, which means the estimated number of trout in the lake is 43.

So, my fishing friend, the correct answer is actually A. 43 trout.

Yes, it is C.

To estimate the number of trout in the lake, we can use a proportion based on the number of tagged trout caught in the second sample.

Let's start by setting up the proportion:

(Number of tagged trout in first sample) / (Total number of trout in the lake) = (Number of tagged trout in second sample) / (Number of trout caught in the second sample)

In the first sample, the worker caught, tagged, and released 120 trout. In the second sample, she caught 84 trout and found tags on 30 of them.

120 / (Total number of trout in the lake) = 30 / 84

Now, we can cross-multiply and solve for the total number of trout in the lake:

30 * (Total number of trout in the lake) = 120 * 84
30 * (Total number of trout in the lake) = 10080
Total number of trout in the lake = 10080 / 30
Total number of trout in the lake = 336

So, the estimated number of trout in the lake is 336, which corresponds to option C.

To estimate the number of trout in the lake, we can use a proportion based on the ratio of tagged trout to total trout in the second catch.

Let's set up the proportion:
(Tagged trout / Total trout in second catch) = (Total tagged trout / Estimated total trout in the lake)

We know that the worker caught 84 trout in the second catch and found tags on 30 of them, so the ratio of tagged trout to total trout in the second catch is 30/84.

Now, we can substitute the values into the proportion:
(30/84) = (120/x)

To solve for x (estimated total trout in the lake), we can cross multiply:
30 * x = 120 * 84

x = (120 * 84) / 30

x ≈ 3360 / 30

x ≈ 112

So, the estimated number of trout in the lake is approximately 112.

The answer choice C. 336 is the closest option to our estimate, so yes, your answer is correct.