A farmer has 1,180 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 $62,600 for the cost of growing his crops. How many acres of each crop should he plant?

Answer + Explication

c+w+s=1080,

45c+60w+50s=57000

i think thats the answer

240 acres is required to grow corn,

480 acres is required to grow wheat

460 acres is required to grow soybeans

Step-by-step explanation:

The farmer has 1180 acres of land. He grows three crops namely corn, wheat and soybeans.

The cost to grow corn per acre of land = $45

The cost to grow wheat per acre of land = $60

The cost to grow soybeans per acre of land = $50

Let the number of acre to grow corn = a

Let the number of acre to grow wheat = 2a

Let the number of acre to grow soybeans = b

He allocated $62600 for the cost of growing these crops.

Total acres = a + 2a + b = 1180

Total acres = 3a + b = 1180 ... (i)

Total cost = 45 (a) + 60 (2a) + 50 (b) = 62600

45a + 120a + 50b = 62600

165a + 50b = 62600 ... (ii)

from equation (i)

b = 1180 - 3a

insert the value of b in equation (ii)

165a + 50 (1180 - 3a) = 62600

165a + 59000 - 150a = 62600

165a - 150a = 62600 - 59000

15a = 3600

divide both sides by 15

a = 3600/15

a = 240

Insert the value of a in equation (i)

3a + b = 1180

3 (240) + b = 1180

720 + b = 1180

b = 1180 - 720

b = 460

240 acres is required to grow corn,

480 acres is required to grow wheat

460 acres is required to grow soybeans