There's no rule. It varies for everyone and for the same person different times. You don't know if you'll succumb to the effects any particular trip on high mountains even if you're well experienced. A party on Kilamanjaro last year did well but the guide got bad with the altitude and he'd been up dozens of times.
Around 12 000 - 14 000 feet is getting toward danger time for most folks but if you move slowly and take care, eat well, drink enough but don't overdo it, most people will be OK. Keeping your pack light helps. Overworking is bad at altitude.
If you get bad, come down a bit but slowly. No rushing.
Rest up a day or two in thicker air,then go up again, slow.
If you're alone keep a constant check on yourself. If with others, keep a check on them and they check you.
Fix up a buddy system. Buddies look after each other.
Teamwork, helping others along, is even more important at high altitudes.
Cusco is at 11 000 feet and it's best to go to Arequipa at 8 000 feet for a couple of days to acclimatise first. Many don't and are OK but one guy while I was there ran for the bus and collapsed after a few paces. I gave a hand (ex Army medic) and found he'd got there by plane that morning straight from Lima which is at at sea level.
I had three days in Arequipa and loved it. One of the best places I have seen anywhere in the world, so following the advice had an extra benefit. I always arrange my own transport as I travel around so I never have a schedule I have to stick to apart from the long haul flight back home.
In Peru people chew coca leaves to help against altitude sickness, even the locals. You can buy coca tea bags called Mate de Coca, (pronounced matay de coca) normally just called mate, in the shops and supermarkets, and bags of coca leaves. It's legal, but processed coca gets you a long jail term.
The hospitality tables in the hotel rooms all have tea, coffee, and mate tea.
When I cracked a tooth in Cusco and the filling came out the pharmacist advised me to chew a couple of coca leaves to plug the gap. Worked a treat and the dentist back home said he wished coca leaves were available here. Did a great job, for around 5 cents.
http://www.cocaine.org/potplant.htm . . . . . . . .
http://www.travelpod.com/travel-blog-entries/plasticrover/southamerica04/1110643920/tpod.html