```python
def vat_back(gross: int, rate: int) -> int:
    """
    Return the price before a whole-percent tax was added to the given gross price.
    
    Args:
    gross (int): The gross price with a whole-percent tax.
    rate (int): The tax rate in whole percent.
    
    Returns:
    int: The price before the tax was added.
    """
    if rate < 0:
        raise ValueError("Tax rate cannot be negative.")
    
    if rate == 0:
        return gross
    
    # Calculate the tax amount
    tax_amount = gross * (rate / 100)
    
    # Calculate the price before tax
    price_before_tax = gross - tax_amount
    
    # Round down to the nearest integer
    return int(price_before_tax)
```