I posted a discussion with my results from the last season of crates. Should be comparable to what you could expect if you also haven't opened any yet.

https://forums.elderscrollsonline.com/en/discussion/306221/crown-gem-conversions-and-the-equivalent-cost-in-dollars-of-an-apex-mount#latest

I averaged 3 gems/crate so it would take 5-6 crates to get to 16.