the anatomy of a persuasive argument

I decided it was time for new shoes. The ones I have currently are already old and I mostly use them everyday. Now I know that it might sound spoiled that I want new shoes because I use mine current ones everyday, and and they are still in decent condition, but I am very grateful and fortunate that my parents, although it is still hard for them, could afford to buy me some. I used the Ethos Pathos Logos Kiros method to do this argument. I started the argument by simply asking them. They said that I already had so many and that it was unnecessary for me to get new ones. I proceeded to use Logos (logic)to tel them that yes, I do have several pairs of shes, but they are for specific sports and can't be used as regular daily shoes. I used Ethos as why I should get new shoes, I take care of them unlike my brother who had gotten a pair the same time I did and he had already gotten a new pair. This convinced them so I waited for the weekend to go buy my new pair of shoes.