A farmer has 1100 acres of land on which he grows corn wheat

A farmer has 1,100 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 $58,450 for the cost of growing his crops. How many acres of each crop should he plant?

corn _________acres

wheat_________acres

soybeans_________acres

Solution

let x=corn

let 2x=wheat

let y= soybeans.

x+2x+y=1100
45x+60(2x)+50y=58450
system of equations
3x+y=1100
45x+120x+50y=58450

3x+y=1100
165x+50y=58450

solving for y

y=1100-3x

substitue

165x+50(1100-3x)=58450
165x+55000-150x=58450

15x=3450
x=230.

subsitute

3(230)+y=1100

690+y=1100
y=410.

remember.
x=corn 2x=wheat y=beans.

230=corn 2(230)=460=wheat and 410=soybeans.

he should plant
230 acres of corn, 460 acres of wheat and 410 acres of soybeans.