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

Question

vladimir1956 [14]

2 years ago

8

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?

Engineering

1 answer:

maw [93] · Answer 1 · 2023-08-25T22:09:16+03:00

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

<h3>How to solve algebra word problem?</h3>

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

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