Word Problem

Question

A farmer has 1,050 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 $55,500 for the cost of growing his crops. How many acres of each crop should he plant?

Answer 1

 

x = acres of corn

y = acres of wheat

z = acres of soybeans

 

 

X + Y + Z = 1050

 

45X + 60Y + 50Z = 55500

 

Y = 2X

 

 

substitutes the third equation into the first and second:

 

 

3X + Z = 1050  --->  Z = 1050 - 3X

165X + 50Z = 55500

165X + 50(1050-3X) = 55500

 

165X + 52500 - 150X = 55500

 

15X = 3000

 

 x = 200

 

y = 400

 

z = 1050 - 3X = 1050 - 600 = 450