Nanh is really into magic tricks and decides to put on a show to buy more magic trick kits and accessories. She sells three types of tickets to the show. Adult tickets are $10, young adult tickets are $8, and child tickets are $4. Nanh sells a total of 21 tickets and brings in $140. The number of child tickets sold is twice the number of young adult tickets sold. Write a system of equations to represent this situation where x is the number of adult tickets sold, y is the number of young adult tickets sold, and z is the number of child tickets sold. How many of each type of ticket did Nanh sell?