Understanding v.a.t. on Commission

Do I think wrongly?

I have to pay 10% v.a.t. When I sell aroom for $100,- incl v.a.t. my income is around $91,-

When I apply for a hypotetically 100% commission.

Booking charges me 100% of $100,- plus 10% v.a.t. =$110,- so $19,- more then my income.

I can get the paid v.a.t. back but I still pay around 9% more then the 100%

I think the commission should be over the room price excluding v.a.t. .Or am I wrong?