A farmer can buy four types of plant food. Each barrel of mix A contains 30 pounds of phosphoric​ acid, 50 pounds of​ nitrogen, and 20 pounds of​ potash; each barrel of mix B contains 30 pounds of phosphoric​ acid, 75 pounds of​ nitrogen, and 30 pounds of​ potash; each barrel of mix C contains 30 pounds of phosphoric​ acid, 25 pounds of​ nitrogen, and 30 pounds of​ potash; and each barrel of mix D contains 60 pounds of phosphoric​ acid, 25 pounds of​ nitrogen, and 50 pounds of potash. Soil tests indicate that a particular field needs 840 pounds of phosphoric​ acid, 825 pounds of​ nitrogen, and 750 pounds of potash. How many barrels of each type of food should the farmer mix together to supply the necessary nutrients for the​ field?