A flower shop sold 225 flowers for Mother's Day. They sold lilies for $1.60 each, roses for $6.15 each, and daisies for $3.50 each. They sold 50 fewer lilies than roses. The sales totaled $960.50. Use x to represent the number of lilies sold, y to represent the number of roses sold, and z to represent the number of daisies sold.
Write a system of three equations that directly models this situation.
Do not substitute values in any equation while writing the system.