Energy and particle conservation in Maxwell-Boltzmann statistics

I was working with a derivation of Maxwell-Boltzmann statistics occupation probability today and I got this problem with the constraints:

We know that the particle number is conserved when we are increasing the value of $N_i$ by a little amount, so we write that, $$sum_{i}^{N}delta N_i=0$$ where $N$ is the total number of particles.

Also, since if the number of particles of a particular energy $E_i$ increases, then by energy conservation, that same energy change has to be accompanied by some other particles, in different quantum states. So, for that we write:
$$sum_{i}^{N}E_i delta N_i=0$$
However, I am not being able to understand this last equation. For example- Suppose we have $1000$ particles with energy $2 eV$ and $2000$ particles with energy $1 eV$, the total energy of the system is $4000 eV$. Now, assuming that $1$ and $2$ $eV$ are the only energies that can be possessed by the particles, let us decrease the number of particles in the state $1 eV$ by $100$. So now we have $900$ particles in the $1 eV$ state, and since the energy of the system has to be conserved, the number of particles increased in the state $2 eV$ is 50.

This is where I start facing problems. The last argument shows that the number of particles having energy $2 eV$ is now $2050$, which, if added to the other ones, gives $2950$ particles, whereas the total number, in the beginning, was $3000$.

What am I missing here?