```python
def tint_mix(volume_a: int, strength_a: int, volume_b: int, strength_b: int) -> int:
    """Calculate the strength of a mixture of two tins of paint, rounded down to a whole percent."""
    if volume_a < 0 or volume_b < 0:
        raise ValueError("Volumes must be non-negative")
    if strength_a < 0 or strength_b < 0:
        raise ValueError("Strengths must be non-negative")
    
    total_volume = volume_a + volume_b
    if total_volume == 0:
        return 0
    
    total_paint = volume_a * strength_a + volume_b * strength_b
    mixture_strength = total_paint // total_volume
    
    return mixture_strength
```