Some business ideas for a 15-year-old include starting a pet care business, offering DJ services, providing freelance creative work, starting a cleaning service, offering gift wrapping services, and babysitting. These businesses can be started with minimal capital and can be run on a part-time basis. Additionally, many of these businesses can be operated from home, making them convenient for teenagers who may have other commitments such as school. It's important to note that some businesses may require a parent or guardian to act as a legal representative for the teenager.