A farmer has 1,300 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 $69,050 for the cost of growing his crops. How many acres of each crop should he plant?
corn ____ acres
wheat ____ acres
soybeans _____ acres

Question

A farmer has 1,300 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 $69,050 for the cost of growing his crops. How many acres of each crop should he plant?
corn  ____  	  acres
wheat ____   	  acres
soybeans   _____ 	  acres

gw2011 · Answer

I got the following answers:

corn=270 acres
wheat=540 acres
soybeans=490 acres

Here is how I arrived at these answers:

Let c=corn
Let w=wheat=2c
Let s=soybeans

45c+120c+50s=69,050  (60 times 2=120c)
c+2c+s=1300

165c+50s=69,050
3c+s=1300

Solving these two equations by eliminating s (multiply second equation by 50)

165c+50s=69,050
150c+50s=65,000

15c=4050
c=270 acres
w=540 acres (270 times 2)
s=490 acres (1300-270-540)