I think an important thing to consider is just how important the activity (in the OP's case, the voice lessons) are to the child. In other words, just how badly is she wanting to do the activity?
For example, the other day I offered to take my DS out for frozen yogurt as a special treat. He said he wanted to go (who doesn't love frozen yogurt?!) but then, when it was time to go, wasn't eager to stop what he was doing. So, I asked him if he *really* wanted to go, and he was wishy-washy. So, together we made the decision that, if it wasn't something he *really* wanted to do, we would just save the money.
Obviously, the kinds of extracurriculars we are discussing here are much more expensive and long-term, but I think the same principle applies. I don't put too much stock in whether the activity has value long-term, but more in what my child gets out of it in the short-term. For example, I know my DD (or any of my kids, for that matter) won't be college athletes, but they both really love spending time with their friends playing sports (and I enjoy the comaraderie with the parents), they get exercise, and they learn about hard work (which they don't get in school), so the costs are worth it for now.
One caveat we have in our family: the disruptions to our family life have to feel worth it to us, as parents.
Also, we're lucky we're not having to choose activities based on how much we can afford, but we're definitely frugal-minded about most things. So, if we're on the fence about how important an activity is or how much someone wants to do it, we definitely won't pay for it.
ETA: I don't know if I answered your original question - sorry! Personally, we're all over the place with expenses. One child has only one very low cost activity, while another has several mid-level costs activities, and the third has several mid-level cost activities plus a few more-expensive camps. So, in our family, we don't have a hard-and-fast rule or limit, which I think was part of your original question. Ours is an ever-changing, ever-reconsidering set of expenses.
Last edited by mnmom23; 04/01/13 05:56 AM.