SOLUTION: 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 dem

Question 1199191: 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?
corn acres
wheat acres
soybeans acres

Answer by ikleyn(52786) (Show Source): You can put this solution on YOUR website!
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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?
~~~~~~~~~~~~~~~~~~

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 =  = 270.


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

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.

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