You need to think of the man and the chair separately. The man has a tension force acting upwards on him, a normal force upwards on him, and his weight downwards. The chair has tension acting upwards, the same magnitude of a normal force downwards, and it's weight downwards. We can exploit that each of the tension forces are the same, as well as the fact that the man and chair will have the same acceleration. Therefore, by Newton's second law,
$$ma=T+N-mg$$ $$Ma=T-N-Mg$$
Where $m$ and $M$ are the masses of the person and the chair respectively.
Since you are given what $m$, $M$, and $N$ are, these are two equations with two unknown values. Note that the 100 lbs corresponds to $N$, not $T$. I will leave the math to you.