How do you dye your hair with koolaid with dark brown hair?

i have black hair, well, jet brown in the winter and dark brown in the summer, but the tips are reg. brown. it just gets lighter in the sun. i have i strip of 5$ burgundy (supposed 2 b purple) from cost cutters in my hair. i was wondering how i could put g koolaid on that strip to stay on for a while. its a lot lighter than my hair, so it should be more noticible, or less. i was going for a dark purple. any help would be great! oh, and my 5 year old sis wants pink in her hair. she has strawberry blonde. should i let her with a dye that'll only stay in for a week, or not at all???