Question 1199191
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A farmer has 1,310 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 $69,550 for the cost of growing his crops. 
How many acres of each crop should he plant?
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<pre>
x  = acres  for corn;

2x = acres for wheat

1310-x-2x = 1310-3x = acres for soybeans  (the rest).


The money equation is

    45x + 60*(2x) + 50*(1310-3x) = 69550  dollars.


This equation is in one unknown, and you can easily solve it

    45x + 120x + 50*1310 - 150x = 69550

    x = {{{(69550-50*1310)/(45 + 120-150)}}} = 270.


<U>ANSWER</U>.  270 acres for corn;  2*270 = 540 acres for wheat, and the rest 1310-270-540 = 500 acres for soybeans.
</pre>

Solved.


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The most interesting and educational lesson from this solution is that
the problem can be solved using one equation in one single unknown.