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Part 1

A farmer can buy four types of plant food. Each barrel of mix A contains

40

pounds of phosphoric acid,

75

pounds of nitrogen, and

20

pounds of potash; each barrel of mix B contains

40

pounds of phosphoric acid,

100

pounds of nitrogen, and

30

pounds of potash; each barrel of mix C contains

40

pounds of phosphoric acid,

25

pounds of nitrogen, and

30

pounds of potash; and each barrel of mix D contains

80

pounds of phosphoric acid,

25

pounds of nitrogen, and

50

pounds of potash. Soil tests indicate that a particular field needs

1,360

pounds of phosphoric acid,

1,000

pounds of nitrogen, and

930

pounds of potash. How many barrels of each type of food should the farmer mix together to supply the necessary nutrients for the field?