## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'hours worked by John' and 'hours worked by Mary'. Let's denote 'hours worked by John' as $x_1$ and 'hours worked by Mary' as $x_2$. The objective function to minimize is $7.35x_1 + 9.07x_2$. The constraints are:
- $0.51x_1 + 0.47x_2 \geq 42$
- $0.51x_1 + 0.47x_2 \leq 79$
- $x_1 - 3x_2 \geq 0$
- $x_1$ and $x_2$ must be whole numbers.

## Step 2: Convert the problem into a symbolic representation
The symbolic variables are:
- $x_1$ for 'hours worked by John'
- $x_2$ for 'hours worked by Mary'

The objective function is: $7.35x_1 + 9.07x_2$

The constraints are:
- $0.51x_1 + 0.47x_2 \geq 42$
- $0.51x_1 + 0.47x_2 \leq 79$
- $x_1 - 3x_2 \geq 0$
- $x_1, x_2 \in \mathbb{Z}$ (integer constraint)

## 3: Represent the problem in the required JSON format
```json
{
    'sym_variables': [('x1', 'hours worked by John'), ('x2', 'hours worked by Mary')],
    'objective_function': '7.35*x1 + 9.07*x2',
    'constraints': [
        '0.51*x1 + 0.47*x2 >= 42',
        '0.51*x1 + 0.47*x2 <= 79',
        'x1 - 3*x2 >= 0',
        'x1, x2 are integers'
    ]
}
```

## 4: Implement the problem using Gurobi
To solve this problem using Gurobi, we need to write Python code that defines the model, sets up the variables and constraints, and then solves the model.

```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name='hours_worked_by_John', vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name='hours_worked_by_Mary', vtype=gurobi.GRB.INTEGER)

    # Set the objective function
    model.setObjective(7.35 * x1 + 9.07 * x2, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(0.51 * x1 + 0.47 * x2 >= 42)
    model.addConstr(0.51 * x1 + 0.47 * x2 <= 79)
    model.addConstr(x1 - 3 * x2 >= 0)

    # Update the model
    model.update()

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print('Optimal solution found.')
        print(f'Hours worked by John: {x1.varValue}')
        print(f'Hours worked by Mary: {x2.varValue}')
        print(f'Objective function value: {model.objVal}')
    else:
        print('No optimal solution found.')

solve_optimization_problem()
```