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A farmer has 12 hectares of land on which he grows corn, wheat, and soybeans. It costs $4500 per hectare to grow corn, $6000 to grow wheat, and $5000 to grow soybeans. Because of market demand the farmer will grow twice as many hectares of wheat as corn. He has allocated $6,375,000.00 for the cost of growing his crops. How many hectares of each crop should he plant?

Respuesta :

The number of hectares of each crop he should plant are; 250 hectares of Corn, 500 hectares of Wheat and 450 hectares of soybeans

How to solve algebra word problem?

He grows corn, wheat and soya beans on the farm of 1200 hectares. Thus;

C + W + S = 12   ----(1)

It costs $45 per hectare to grow corn, $60 to grow wheat, and $50 to grow soybeans. Thus;

45C + 60W + 50S = 63750  -----(2)

He will grow twice as many hectares of wheat as corn. Thus;

W = 2C    ------(3)

Put 2C for W in eq 1 and eq 2 to get;

C + 2C + S = 1200

3C + S = 1200     -----(4)

45C + 60(2C) + 50S = 63750

45C + 120C + 50S = 63750

165C + 50S = 63750    ------(5)

Solving eq 4 and 5 simultaneosly gives;

C = 250 and W = 500

Thus; S = 1200 - 3(250)

S = 450

Read more about algebra word problems at; https://brainly.com/question/13818690

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