Fertilizer is sold in 100 pound bags labelled with the amoun

Fertilizer is sold in 100 pound bags labelled with the amount of nitrogen (N), phosphoric acid (P2O5), and potash (K2O) present. The mixture of these nutrients varies from one type of fertilizer to the next. For example, a 100 pound bag of Vigoro Ultra Turf fertilizer contains 29 pounds of nitrogen, 3 pounds of phosphoric acid, and 4 pounds of potash. Another type of fertilizer, Parker\'s Premium Starter, has 18 pounds of nitrogen, 25 pounds of phosphoric acid, and 6 pounds of potash per 100 pounds. Determine the amount of each type required to yield a mixture containing the 105 pounds of nitrogen, 34 pounds of phosphoric acid, and 18 pounds of potash.

Solution

100 pound vigoro - 29 pound N , 3 P , 4 K

100 pound parker -   18 pound N , 25 P , 6 K

let vigoro be x pound

parker be y

N - 0.29 x + 0.18 y = 105

P - 0.03 x + 0.25 y = 34

K - 0.04 x + 0.06 y = 18

X =300,Y =100

so mixture contains 300 pound of Vigoro and 100 pounds of Parker