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!