Question 1139504
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{{{highlight(cross(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?
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            This problem is to be solved using one equation in one single unknown.



<pre>
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                        = {{{11000/80}}} = 137.5


<U>ANSWER</U>.  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.
</pre>

Solved, explained and completed.


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To see many other similar solved problems, look into the lesson

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&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/equations/HOW-TO-algebreze-and-solve-these-problems-using-one-eqn-in-one-unknown.lesson>HOW TO algebreze and solve these problems using one equation in one unknown</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/equations/Challenging-word-problems-to-solve-using-a-single-linear-equation.lesson>Challenging word problems to solve using a single linear equation</A> 

in this site, and learn the subject from there.



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The major lesson to learn from my post is <U>THIS</U> :


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


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