Answer
The elevator's acceleration must have been between $0.771 ~m/s^2$ and $1.03 ~m/s^2$
Work Step by Step
The line holding the 2.10-kg ball broke. Let's suppose that the elevator's acceleration caused the tension force in the fishing line to be equal to the limit of 22.2 N:
$ma = F_T - mg$
$a = \frac{F_T - mg}{m} = \frac{22.2 ~N - (2.10 ~kg)(9.80 ~m/s^2)}{2.10 ~kg}$
$a = 0.771 ~m/s^2$
Since the fishing line broke, the elevator's acceleration must have been at least $a = 0.771 ~m/s^2$.
The line holding the 2.05-kg ball didn't break. Let's suppose that the elevator's acceleration caused the tension force in the fishing line to be equal to the limit of 22.2 N.
$ma = F_T - mg$
$a = \frac{F_T - mg}{m} = \frac{22.2 ~N - (2.05 ~kg)(9.80 ~m/s^2)}{2.05 ~kg}$
$a = 1.03 ~m/s^2$
Since the fishing line didn't break, the elevator's acceleration must have been at most $a = 1.03 ~m/s^2$
Therefore, the elevator's acceleration must have been between $0.771 ~m/s^2$ and $1.03 ~m/s^2$.