To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining variables and formulating the objective function and constraints algebraically.

Let's denote:
- \(x_1\) as the number of regular passes sold,
- \(x_2\) as the number of premium passes sold.

The objective is to maximize profit. Given that the profit per regular pass is $40 and per premium pass is $90, the objective function can be written as:
\[ \text{Maximize:} \quad 40x_1 + 90x_2 \]

Now, let's consider the constraints based on the problem description:
1. The movie theatre can sell at most 500 passes in total:
\[ x_1 + x_2 \leq 500 \]
2. At least 100 passes are reserved to be premium:
\[ x_2 \geq 100 \]
3. At least 3 times as many people prefer to buy regular passes than premium passes:
\[ x_1 \geq 3x_2 \]

Additionally, we should note that \(x_1\) and \(x_2\) cannot be negative since they represent the number of passes sold:
\[ x_1 \geq 0, \quad x_2 \geq 0 \]

The symbolic representation in JSON format is therefore:

```json
{
    'sym_variables': [('x1', 'number of regular passes'), ('x2', 'number of premium passes')],
    'objective_function': '40*x1 + 90*x2',
    'constraints': [
        'x1 + x2 <= 500',
        'x2 >= 100',
        'x1 >= 3*x2',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

To solve this problem using Gurobi in Python, we can write the following code:

```python
from gurobipy import *

# Create a new model
m = Model("Movie_Theatre_Optimization")

# Define variables
x1 = m.addVar(name="regular_passes", lb=0)
x2 = m.addVar(name="premium_passes", lb=0)

# Set the objective function
m.setObjective(40*x1 + 90*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + x2 <= 500, name="total_passes_limit")
m.addConstr(x2 >= 100, name="premium_passes_minimum")
m.addConstr(x1 >= 3*x2, name="regular_vs_premium_ratio")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution found: {m.objVal}")
    print(f"Number of regular passes: {x1.x}")
    print(f"Number of premium passes: {x2.x}")
else:
    print("No optimal solution found")
```