## Step 1: Define the symbolic representation of the problem
Let's denote the number of adult tickets as $x_1$ and the number of children's tickets as $x_2$. The objective is to maximize profit, which is $3x_1 + x_2$. The constraints are:
- The bus can carry at most 80 people: $x_1 + x_2 \leq 80$
- The bus reserves at least 15 tickets for children: $x_2 \geq 15$
- At least 3 times as many tickets sold are adult tickets than children's tickets: $x_1 \geq 3x_2$
- Non-negativity constraints: $x_1 \geq 0, x_2 \geq 0$

## 2: Convert the problem into a symbolic representation
The symbolic representation is:
```json
{
'sym_variables': [('x1', 'adult tickets'), ('x2', 'children\'s tickets')],
'objective_function': '3*x1 + x2',
'constraints': [
    'x1 + x2 <= 80',
    'x2 >= 15',
    'x1 >= 3*x2',
    'x1 >= 0',
    'x2 >= 0'
]
}
```

## 3: Translate the symbolic representation into Gurobi code
Now, let's translate this into Gurobi code in Python:

```python
import gurobi

def solve_bus_ticket_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x1 = model.addVar(name="adult_tickets", lb=0, ub=None, vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="children_tickets", lb=0, vtype=gurobi.GRB.INTEGER)

    # Objective function: maximize 3*x1 + x2
    model.setObjective(3*x1 + x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(x1 + x2 <= 80, name="total_capacity")
    model.addConstr(x2 >= 15, name="children_tickets_reserved")
    model.addConstr(x1 >= 3*x2, name="adult_to_children_ratio")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: adult tickets = {x1.varValue}, children's tickets = {x2.varValue}")
    else:
        print("No optimal solution found")

solve_bus_ticket_problem()
```