Ballpark, 15. Many variables. Many many variables.
If you can put the switch in the middle and keep all the cable runs under 100m then a single MS120-24P would do it. Otherwise, you might need a pair of them linked by fibre.
I'm just giving you rough guides. I think you should get a Cisco partner to come and help you with this. You can find someone close to you using the Cisco partner locator.