One type of lawn fertilizer consists of a mixture of nitrogen, N. phosphorus, P, and potassium, K. An 80-pound sample contains 8 more pounds of nitrogen and phosphorus than of potassium. There is nine times as much potassium as phosphorus. 

(a) Write a system of three equations whose solution gives the amount of nitrogen, phosphorus, and potassium in this sample. 

(b) Solve the system of equations.