I have adult acne, have visited several dermatologists, and have tried a wide variety of prescription and over the counter acne treatments - but none of them have worked as well as the following regime...which also happens to be frugal.
Quite by accident, I discovered that antibacterial soap (I like Dial bar soap), used regularly on the areas of my body where I tend to get acne, prevents almost all breakouts. Really. I even use it on my face, every other day.
On the rare occasion I do need spot acne treatment, I use Clean & Clear's Persa Gel, and continue to use antibacterial soap, too. Usually, I need only one or two treatments of the gel. When I don't want to wash my face with antibacterial soap (perhaps because I think it might be too drying), I use Mary Kay's Velocity facial cleaner. One container of this lasts me between four and six months.
Doctors rarely recommend antibacterial soap for the face - but only because it might be drying (which can cause more acne). However, those of us with persistent acne usually have oily skin, so as long as you pay attention to whether your skin is becoming too dry, antibacterial soap is a super cheap way to keep acne at bay.
Try it for yourself or your teen.