Fertilizer is sold in bags labelled with three numbers that indicate the amount

Question

Fertilizer is sold in bags labelled with three numbers that indicate the amount of nitrogen (N), phosphoric acid (P_2O_5), and potash (K_2O) present. A bag of Vigoro Ultra Turf has the numbers "29-3-4," which means that 100 pounds of this fertilizer contains 29 pounds of nitrogen, 3 pounds of phosphoric acid, and 4 pounds of potash. A bag of Parker's Premium Starter has 18 pounds of nitrogen, 25 pounds of phosphoric acid, and 6 pounds of potash per 100 pounds. (See the discussion at the start of the section.) Determine the amount of each type required to yield a mixture containing the given amounts of nitrogen, phosphoric acid, and potash. 242 pounds of nitrogen, 187 pounds of phosphoric acid, and 58 pounds of potash. Vigoro bags Parker's bags

Explanation / Answer

Vigro Ultra : x bags

So, nitrogen = 0.29x ; phos = 0.03x ; potash = 0.04x

Parker's Premium : y bags

So, nitrogen = 0.18y ; phos = 0.25y ; potash = 0.06y

0.29x + 0.18y = 242

0.03x +0.25y = 187

solve the above equations:

Vigro Ultra :x = 400 bags ; Parker's Premium y = 700 bags

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