You have a 64 GB server to use as a virtualization host. You have thirty-two application servers that you plan to P2V to this host. Each application server is currently on a physical server that has 4 GB of memory. The application servers all run Windows Server 2008.

*Very crucial information Note: do not calculate in any overhead.*

1. Without taking advantage of any memory optimization techniques, what is the maximum number of virtual machines you can host on your server? (I answered 32 as a guess because I haven't figured out the math yet)
2. With page sharing and ballooning you can take advantage of memory overcommit. If you overcommit memory at a 1.25:1 ratio, how many virtual machines can you now host? (I multiplied 32 x 1.25, again I just don't know which variables from the word problem are which variables in the math)
3. While gathering baseline performance metrics for the move to the virtual environment, you find that on average, each system is actually using only 1 GB of memory. Keeping the same overcommit ratio, how many virtual machines can be hosted? (i got 160 here)
4. You decide to leave some additional memory available for growth or emergency. At a 90 percent utilization limit, how many virtual machines can you have? (I got 144 here)

I need the math explained step by step please!