```python
def vat_back(gross: int, rate: int) -> int:
    """
    Calculate the original price before adding a given tax rate.

    Parameters:
    gross (int): The gross price including tax.
    rate (int): The tax rate as a percentage.

    Returns:
    int: The original price before tax.
    """
    if rate < 0:
        raise ValueError("Tax rate cannot be negative.")
    
    # Calculate the original price by dividing the gross price by (1 + rate/100)
    original_price = gross / (1 + rate / 100)
    
    # Round down the original price to the nearest integer
    return int(original_price)
```