```python
def vat_back(gross: int, rate: int) -> int:
    """Return the pre-tax price given a gross price and tax rate.

    The gross price already includes the tax. The tax rate is applied to the
    pre-tax price to produce the gross price. Solving for the pre-tax price
    gives: pre_tax = gross / (1 + rate).

    The result is rounded down (floor division).
    """
    return gross // (rate + 1)
```