There actually is a proper way to cut a cake, and a lot of caterers don't follow this, it's a tremendous pet peeve of mine, because I can get more than 22 slices out of an 8 inch round cake... so there is no reason that a standard 3 tier cake can't fee 150 people! From a 10 inch cake, you should be able to get 50 slices.
Ask your Pastry Chef if you can pay by slice rather than per person, or vise versa depending on where you feel you'll be able to get the most bang for your buck!