Solve the problem by writing and solving a suitable system of equations. 17) A s

Question

Solve the problem by writing and solving a suitable system of equations. 17) A shopkeeper orders 54 pounds of cashews and peanuts. If the amount of cashews he 17) orders is 12 pounds less than the amount of peanuts, how many pounds of peanuts did he order? olve the problem. 18) According to an agricultural report, the amounts of nitrogen (Ib/acre), phosphate (lb/acre), 18) and labor (Ib/acre), needed to grow three different vegetables are given by the following table Vegetable A Vegetable BI Vegetable C Nitrogen Phosphate 140 Labor 120 170 100 4.4 4.8 4.6 If a farmer has 260 acres, 35,600 pounds of nitrogen, 30,800 pounds of phosphate, and 1208 hours of labor, can he use all of his resources completely? If so, how many acres should he allot for each crop?

Explanation / Answer

17) Let x be Pounds of peanuts he ordered

and y be pounds of cashews he ordered

x + y = 54

y = x- 12

subsituting second equation into first, we get

2x = 66

x = 33

y = 33 - 12 = 21

Peanuts = 33, cashew = 21

18)

Let x be the Vegetable A, y be the vegetable B and z be the vegetable C

Accoring to the data given, linear equation as follows

x + y + z = 260

120 x + 150y + 170 z = 35,600

140x + 100y + 80z = 30,800

4.8x + 4.4 y + 4.6 z = 1208

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