SOLUTION: I think this is a system of equations question. A farmer plants soybeans, corn, and wheat and rotates the planting each year on his 500 acre farm. In a particular year, the pro

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Question 1139505: I think this is a system of equations question.
A farmer plants soybeans, corn, and wheat and rotates the planting each year on his 500 acre farm. In a particular year, the profits from his crops were $120 per acre of soybeans, $100 per acre of corn, and $80 per acre of wheat. He plants twice as many acres of corn as soybeans.
How many acres did he plant with each crop the year he made a total profit of $51,000?
Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website!

It COULD be a system of equations problem; as such, it would be a good exercise in solving such problems.

However, it is much easier to solve if you write and solve a single equation using a single variable.

It will take a little extra time to figure out how to write the single equation in a single variable; but solving that single equation will take far less time than solving a system of three equations in three variables.

Here is how you would probably set up the problem using three variables....

Let x = acres of soybeans
Let y = acres of corn
Let z = acres of wheat

Then

(1) x+y+z = 500 (the total acreage is 500)
(2) y = 2x (twice as many acres of corn as soybeans)
(3) 120x + 100y + 80z = 51000 (his profit is $51,000)

You would probably replace "y" with "2x" in (1) and (3) and then use elimination to solve for either x or z, and then proceed from there....

Here is how you could set up the equation using a single variable:

Let x = acres of soybeans
Then 2x = acres of corn (twice as many acres of corn as soybeans)
And (500-3x) = acres of wheat (the total acreage is 500; 3x of that is corn or soybeans)

Then the single equation is

ANSWER: x=137.5 acres of soybeans; 2x = 275 acres of corn; (500-412.5) = 87.5 acres of wheat