Formulate a system of equations for the situation below and solve. Lawnco produc

Question

Formulate a system of equations for the situation below and solve. Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade A fertilizer contains 17 lb of nitrogen, 6 lb of phosphate, and 5 lb of potassium. A 100-lb bag of grade B fertilizer contains 20 lb of nitrogen and 4 lb each of phosphate and potassium. A 100-lb bag of grade C fertilizer contains 24 lb of nitrogen, 3 lb of phosphate, and 6 lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if 26, 400 lb of nitrogen, 4900 lb of phosphate, and 6200 lb of potassium are available and all the nutrients are used? grade A _____ bags grade B _____ bags grade C _____ bags

Explanation / Answer

Let,x, y and z denotes the bag containing grade A fertilizer,grade B fertilizer and grade C fertilizer resp.

From the question,we can form these equations,

17x+20y+24z=26,400 ----------> i

6x+4y+3z=4900 ------------------> ii

5x+4y+6z=6200 ----------------> iii

Solve i and ii to get an equation iv.Then solve ii and iii,to get an equation v.Then solve iv and v equation to get the result.

Therefore,by solving these equations,we get the value of x,y and z as 200,550 and 500.

Hence,there are 200 Grade A bags

550 Grade B bags and

500 Grade C bags

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