Afarmer 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?

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

56

step-by-step explanation:

step-by-step explanation: