A farmer has 1,170 acres of land on which he grows corn, wheat, and soybeans. It costs $45 per acre to grow corn, $60 to grow wheat, and $50 to grow soybeans. Because of market demand the farmer will grow twice as many acres of wheat as of corn. He has allocated $62,250 for the cost of growing his crops. How many acres of each crop should he plant?

a. corn acres

b. wheat acres

c. soybeans acres

Question

Mathematics

Priscilla Murray

24 February, 20:14

A farmer has 1,170 acres of land on which he grows corn, wheat, and soybeans. It costs $45 per acre to grow corn, $60 to grow wheat, and $50 to grow soybeans. Because of market demand the farmer will grow twice as many acres of wheat as of corn. He has allocated $62,250 for the cost of growing his crops. How many acres of each crop should he plant?

a. corn acres

b. wheat acres

c. soybeans acres

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Answers (1)

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Marlie Valdez · Answer 1

Corn Land = 250 Acres; Wheat Land = 500 Acres; Soybean Land = 420 Acres

Step-by-step explanation:

Let the number of acres allocated to corn = c

So, no. of acres allocated to wheat = twice of corn = 2c

Total land for farming = 1170 acres

So, soybean allocated acres = 1170 - c - 2c = 1170 - 3c

Total Cost = Σ [Cost per acre of each crop x No. of Acres allocated to it ]

62250 = 45c + 60 (2c) + 50 (1170 - 3c)

62250 = 45c + 120c + 58500 - 150c

62250 - 58500 = 15c

3750 = 15c

c = 3750 / 15

c = 250 [Corn Allocated Land]

Wheat allocated land = 2c = 2 (250) = 500

Soybean allocated land = 1170 - 3c = 1170 - 3 (250) = 1170 - 750 = 420