Question 1149820
A farmer has 1,080 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 $57,300 for the cost of growing his crops.
 How many acres of each crop should he plant?
:
let c = acres in corn
let w = acres in wheat
let s = acres in soy bean
:
write an equation for each statement
:
"A farmer has 1,080 acres of land on which he grows corn, wheat, and soybeans."
c + w + s = 1080
" It costs $45 per acre to grow corn, $60 to grow wheat, and $50 to grow soybeans.".."He has allocated $57,300 for the cost"
45c + 60w + 50s =  57300
"Because of market demand the farmer will grow twice as many acres of wheat as of corn." 
w = 2c
:
replace w with 2c in the first two equations
c + 2c + s = 1080
3c + s = 1080
and
45c + 60(2c) + 50s = 57300
45c + 120c + 50s = 57300
165c + 50s = 57300
simplify, divide equation by 50
3.3c + s = 1146
use elimination on these two equation
3.3c + s = 1146
3c  +  s = 1080
--------------------subtraction eliminates s, find c
.3c + 0 = 66
c = 66/.3
c = 220 acres in corn
then
w = 2(220)
w = 440 acres in wheat
then
1080 - 220 - 440 = 420 acres in soybeans
:
:
Check this in the statement:
" It costs $45 per acre to grow corn, $60 to grow wheat, and $50 to grow soybeans.".."He has allocated $57,300 for the cost"
45(220) + 60(440) + 50(420) =
9900 + 26400 + 21000 = 57300