Aunt Alice gave each of her threee nieces a number of silver dollars equal to their ages. The youngest felt that this was unfair. They agreed to redistribute the money. The youngest would split half her silver dollars evenly with the other two sisters. The middle sister would then give each of the others 4 silver dollars. Finally, the oldest was to split half of her dollars equally between the two younger sisters. After exchanging the money, each girl had 16 silver dollars. How old were each of the sisters?