Three types of shirts sold at a store cost $9.00, $11.00, and $12.50. One day, the store sells a total of 23 shirts and makes $243 on the sales. Twice as many shirts were sold for $12.50 than were sold for $11.00. If x represents $9.00 shirts, y represents $11.00 shirts and z represents $12.50 shirts, how many of each type of shirt were sold?

Write a system of equations to represent this situation and then solve the system.