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 1139504: 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 ikleyn(52787) About Me  (Show Source):
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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?
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            This problem is to be solved using one equation in one single unknown. 


Let x be the area for soybeans (in acres).

Then the area for corn is  (2x)  acres, and the area for wheat is the rest  (500-x-2x) = (500-3x) acres.


His total profit is then


    120x + 100*(2x) + 80*(500-3x) = 51000   dollars.


Simplify and solve for x


    120x + 200x + 40000 - 240x = 51000


    80x                        = 51000 - 40000

    80x                        = 11000

      x                        = 11000%2F80 = 137.5


ANSWER.  137.5 acres for soybeans;  twice of it, 2*137.5 = 275 acres for corn,  and the rest, 500 - 137.5 - 275 = 87.5 acres for wheat.

Solved, explained and completed.

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To see many other similar solved problems, look into the lesson
    - Advanced word problems to solve using a single linear equation
    - HOW TO algebreze and solve these problems using one equation in one unknown
    - Challenging word problems to solve using a single linear equation
in this site, and learn the subject from there.


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The major lesson to learn from my post is THIS : 

    This problem is designed, is intended, and is expected to be solved using one equation in one single unknown.


Happy learning !


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