(Solved): Fertilizer is sold in 100 pound bags labelled with the amount of nitrogen ( N), phosphoric acid ( ...

Fertilizer is sold in 100 pound bags labelled with the amount of nitrogen ( $$\mathrm{N})$$, phosphoric acid ( P2O5), and potash ( $$\mathrm{K}2\mathrm{O})$$ 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 119 pounds of nitrogen, 128 pounds of phosphoric acid, and 34 pounds of potash. The mixture contains pounds of Vigoro, and pounds of Parker's. Hint: Let $$x_1$$ be the amount of 100 pound bags of Vigoro, and $$x_2$$ the amount of 100 pound bags of Parker. Set up and solve the system in the unknowns $$x_1$$ and $$x_2$$ and then multiply the solution by 100 to find the number of pounds.