The ratio of floor seats to balcony seats in a theaters is 20: 1. does this theater have more floor seats or more balcony seats? how do you know? show work! !

Yes, this theater has more floor seats than balcony seats simply because of the ratio. Your answer is actually in the question. For example, if you have 100 floor seats, then according to the ratio you should only have 5 balcony seats.  So yes, there are more floor seats than balcony seats.