We had a similar question for the addPerson function and the answer received was pretty open to interpretation. Since we just covered Abstraction and all the other pillars, it seems to make sense that if we can write one function that's private or does something without the user having to know how it works then it would be okay to implement it in our programs. I have a bunch of small methods that take care of little things. I had a similar idea to create the find method first but created two separate codes for it.
If you managed to do it, then more power to you.

You should have both. One method's job is to locate a Person and their information, the other is to find and delete a Person and their information. 

Nothing says you can't use your find function to help implement your delete function. With any data structure find and delete are always separate functions. Look at a Stack with its peek and pop functions or ArrayList with its find and remove functions.