Problema Solution
A farmer has 1,320 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 $70,500 for the cost of growing his crops. How many acres of each crop should he plant?
Answer provided by our tutors
let
x = acres of corn
y = acres of wheat
z = acres of soybeans
a farmer has 1,320 acres of land on which he grows corn, wheat, and soybeans:
x + y + z = 1320
the farmer will grow twice as many acres of wheat as of corn:
y = 2x
he has allocated $70,500 for the cost of growing his crops:
45x + 60y + 50z = 70500
by solving the system of equations:
x + y + z = 1320
y = 2x
45x + 60y + 50z = 70500
we find:
x = 300 acres
y = 200 acres
z = 420 acres
click here to see the step by step solution of the system of equations:
he should plant 300 acres of corn, 200 acres of wheat and 420 acres of soybeans.