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

Cornelius Lloyd

Mathematics

7 October, 04:57

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

+1

Answers (1)

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Kaitlin Bullock · 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