Why not? My wife rides a mid-80's Schwinn Traveller 12 speed that I bought for her off a guy for $35 and this bike looked like it just came off the showroom floor - I don't think it had ever been ridden.
I also got a Schwinn Caliente 10 speed from the same guy for $30 for my son. Tires & tubes cost that much - both bikes were great deals and my wife and son enjoy riding them.
Mark