Where did the rabbits go?

The number of eagle = x, the number of rabbit = y, the number of flamingo = z.
After 4 days, the total legs are :
2x + 4 + z = 32 since there are x eagles, 1 rabbit and z flamingos.
2x + z = 28 ........ equation (1)
In first day, the total legs are :
2x + 4y + z = 128 since there are x eagles, y rabbit, and z flamingos.
2x + z = 128 - 4y ........... equation (2)
Solving both equation : 128 - 4y = 28
$\boxed{y = 25}$
Remember that each day, each eagle ate 2 rabbit. So, the number of rabbit eaten after 4 days are 24.
y = 8x + 1. $\boxed{x = 3}$
Using equation (1), with x=3, $\boxed{z = 22}$
Thus, the number of flamingos are 22.

Over the period of 4 days, the number of legs reduced by $128-32=96$

This meant that $96/4=24$ rabbits were eaten.

Hence, $6$ rabbits were eaten in one day and thus, there are $6/2=3$ eagles in the cage.

As such, we can conclude that there were 3 eagles, 25 rabbits, and 22 flamingos at the start.

Let's let the number of eagles= "a" first. Since each of the eagles ate two rabbits each day in 4 days, we know that the eagles ate 2x4xa rabbits in total. Since there are only 1 rabbit left in the cage after 4 days, the number of rabbits at first will be 2x4xa + 1. Now let's build an equation: we can find the number of rabbits eaten by subtracting the amount of legs after 4 days from the number of rabbits in the cage at first divided by 4 since the the rabbits each have 4 legs so: 128-32=(2x4xa)4 in which we get a= 3 now that we know there are 3 eagles, we know the number of rabbits by substituting 3 for "a" in 2x4xa + 1 in which we get 25 rabbits. So to find the number of flamingos, we subtract the numbers of eagles and rabbits from the 50 in which we get 22.