The question says save, not kill. You'd be saving someone by selling your stereo and donating the money. You'd be saving Dave the starving african. I find it strange that people, presumably with stereos, would save the stranger but not the pet. Perhaps peoples answers would be different if you never actually saw the stranger? What if someone came to you, showed you a picture of Dave and said that by some hypotheical magic going and getting your pet put down would save his life?
If you killed your pet now, imagine the people you could save with the money you wouldve spent on pet food and vet bills.