Question

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, Parkerâs 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 177 pounds of nitrogen, 134 pounds of phosphoric acid, and 42 pounds of potash.

Answer 1

You need to add 3 100 pound bags of Parkerâs Premium Starter and 5 100 pound bags of Vigoro Ultra Turf fertilizer

Step-by-step explanation:

You can obtain 3 equations. One for each compound:

For N:

177 pounds = 29x + 18y (1)

-Where x are bags of Vigoro Ultra Turf fertilizer and y are bags of Parkerâs Premium Starte-

For P₂O₅:

134 pounds = 3x + 25y (2)

For K₂O:

42 pounds = 4x + 6y (3)

Replacing (1) in (2):

134 = (531/29 - 54y/29) + 25y

3355/29 = 671y/29

y = 5 bags

Thus,

x = 3 bags

You can replace in each equation to prove that this is the right result.

I hope it helps!