So tuition has tripled, and it's all because of the administrative budget, which is a whopping 15% of expenditures?
1) Suppose the government sponsors $100 out of every student's $103 tuition.
2) Suppose that $3 of that $103 tuition goes towards the beaurocracy.
3) Suppose beaurocracy costs somehow increase to $9, from $3 (and that all other costs remain fixed).
Outcome: Student tuition is now $109, $100 of which is paid for by the government. The students' share of the tuition, however, has tripled from $3 to $9. I doubt the percentages work out anything like that in the real world, though.
And on an entirely unrelated note, a fun quote: "Bureaucracy expands to meet the needs of the expanding bureaucracy."
IIRC, the real cost is often building, and IT. There's also money getting wasted by academics, because they have to follow too many rules. If you give academics a budget, and tell them to spend it wisely, they will probably do so. Give them a list of rules, and they will follow the rules, even if it means they waste a lot of money.