The Intel(R) Core(TM) 2 Duo T7100 is definitely 64 bit.
All core to Duo are.
I just entered it in google and had a few thousand hits on that thing.
You say you want to install it on "her" machine?
Please be careful!! backup everything! Favorites, Address Book, Emails, and email accounts, and of course all the files.
Or you will be asking for a good marriage counselor next.