One bow = 4 cheers.

4 cheers = 8 hops.

8 hops = 24 twitches.

24 twitches = 240 claps.

240/7 = 34.28

Since you can't have a fraction of a person, there must have been at least 35 people.

BONUS!

100 people = 700 claps.

700 claps = 70 twitches.

70 twitches = 23 hops. (You can't have .3 of a hop)

23 hops = 11 cheers. (You can't have half of a cheer)

11 cheers = 2 bows. (You can't have three-quarters of a bow)

At most, they will bow twice.