Chapter 4.3, Problem 85E

Plant food. 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 $30$ pounds of potash; each barrel of mix $B$ contains $30$ pounds of phosphoric acid. $75$ Pounds of nitrogen, and $20$ pounds of potash; each barrel of mix $C$ contains 30 pounds of phosphoric acid. $25$ pounds of nitrogen, and $20$ 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 $900$ pounds of phosphoric acid, $750$ pounds of nitrogen, and $700$ pounds of potash. How many barrels of each type of food should the farmer mix together to supply the necessary nutrients for the field?