Answer:
240 acres is required to grow corn,
480 acres is required to grow wheat
460 acres is required to grow soybeans
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