Question

A horticulturist wants to improve the soil quality in a garden by adding 120 pounds of nitrogen and 54 pounds of potassium. A pack of organic fertilizer contains 2 pounds of nitrogen and 3 pounds of potassium, and a pack of inorganic fertilizer contains 6 pounds of nitrogen and 2 pounds of potassium. How many packs of each type of fertilizer does the horticulturalist need to use? (Hint Write an equation for the total amount of nitrogen (120 pounds) obtained by adding the packs of both the fertilizers and another equation for the total amount of potassium (54 pounds) obtained by adding the packs of both the fertilizers.)

A organic fertilizer: 24 packs; inorganic fertilizer: 12 packs

B. organic fertilizer: 14 packs; inorganic fertilizer: 6 packs

C organic fertilizer: 15 packs; inorganic fertilizer: 8 packs

D. organic fertilizer: 9 packs; inorganic fertilizer: 17 packs

Е. organic fertilizer: 6 packs; inorganic fertilizer: 18 packs​

Answer 1

x and y are the packs of organic and inorganic fertilizer, respectively.

pounds of nitrogen added = 2x + 6y = 120

pounds of potassium added = 3x + 2y = 54

eliminate the y terms. subtract the first equation from 3 times the second equation.

9x + 6y = 162

-2x - 6y = -120

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7x = 42

x = 6

y = 18