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, Parkerâ'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 134 pounds of nitrogen, 37 pounds of phosphoric acid, and 22 pounds of potash.

Answer 1

4 pounds of of Vigoro Ultra Turf fertilizer and 1 pound of Parkera's Premium Starter will yield the required mixture.

Explanation:

In bag of Vigoro Ultra Turf fertilizer:

29 pounds of nitrogen, 3 pounds of phosphoric acid, and 4 pounds of potash

In bag of Parkera's Premium Starter:

18 pounds of nitrogen, 25 pounds of phosphoric acid, and 6 pounds of potash

Let the mass of Vigoro Ultra Turf fertilizer = x

Amount of nitrogen in x amount = 29 x

Amount of phosphoric acid in x amount = 3x

Let the mass of Parkera's Premium Starter= y

Amount of nitrogen in y amount = 18 y

Amount of phosphoric acid in y amount = 25 y

Amount of nitrogen in desired mixture formed by combing x and y fertilizers bag : 134 pounds

29 x + 18 y = 134 ..[1]

Amount of phosphoric acid in desired mixture formed by combing x and y fertilizers bag : 37 pounds

3x + 25 y = 37 ..[2]

Solving [1] anf [2] by substitution method :

`x=(134-18y)/(29)`

`3* (134-18y)/(29)+25y=37`

y = 1

`x=(134-18y)/(29)=4`

4 pounds of of Vigoro Ultra Turf fertilizer and 1 pound of Parkera's Premium Starter will yield the required mixture.