to determine the number of trout in a lake, a conservationist catches 111 trout,tags them throws them back into the lake.later 28 throw are caught. 14 of them are tagged. how many trout would be conservationist expect to be in the lake?'

Well, let's put our fishing hats on and do some calculations! If the conservationist initially caught 111 trout, tagged them, and threw them back into the lake, then we can assume that the proportion of tagged trout in the lake is 111:111, right? Now, if the conservationist catches 28 more trout and finds that 14 of them are tagged, we can set up a simple proportion:

111 (initially tagged trout) : 111 (initially caught trout) = 14 (tagged trout caught later) : 28 (total trout caught later)

Now, let's cross-multiply and solve for x, the number of trout in the lake:

111 * 28 = 111 * x

Simplifying this equation, we get:

3096 = 111x

Dividing both sides by 111:

x ≈ 27.9

So, based on this calculation, we'd expect approximately 27.9 trout (but let's round it up to 28 to avoid any half-fish) in the lake. Clown-approved math for the win!

To determine the estimated number of trout in the lake, we can set up a proportion using the ratio of tagged trout in the second catch to the total number of trout in that catch. We can then use this proportion to estimate the total number of trout in the lake.

Let's break down the information provided:

1. The conservationist caught a total of 111 trout in the first catch and tagged all of them.
2. Later, in the second catch, the conservationist caught a total of 28 trout, and out of those, 14 were tagged.

Now, let's set up the proportion:

Number of tagged trout in the second catch / Total number of trout in the second catch = Number of tagged trout in the lake / Total number of trout in the lake

We can substitute the values we know:

14 / 28 = 111 / x

To solve for x (total number of trout in the lake), we can cross-multiply:

14x = 28 * 111

Now, we can simplify:

14x = 3108

Dividing both sides by 14:

x = 3108 / 14

x ≈ 222

Therefore, the conservationist would expect there to be approximately 222 trout in the lake.