Question 145874: A farmer has 1000 acres of land on which he plans to grow corn, wheat, and soybeans. The cost of cultivating these crops is $28 per acre for corn, $40 per acre for wheat, and $32 per acre for soybeans. If the farmer wishes to use all his available land and his entire budget of $30,000, and if he wishes to plant the same number of acres of corn as wheat and soybeans combined, how many acres of each crop can he grow?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A farmer has 1000 acres of land on which he plans to grow corn, wheat, and soybeans. The cost of cultivating these crops is $28 per acre for corn, $40 per acre for wheat, and $32 per acre for soybeans. If the farmer wishes to use all his available land and his entire budget of $30,000, and if he wishes to plant the same number of acres of corn as wheat and soybeans combined, how many acres of each crop can he grow?
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Let; c = corn; w = wheat; s = soybeans (in acres)
:
total acres equation:
c + w + s = 1000
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Total cost equation:
28c + 40w + 32s = 30000
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It says,"same number of acres of corn as wheat and soybeans combined,"
c = w + s
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In the total acres equation, we can substitute c for w + s
c + c = 1000
c = 1000/2
c = 500 acres of corn
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Therefore:
w + s = 500
w = (500-s)
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Substitute 500 for c and (500-s) w in the cost equation
28(500) + 40(500-s) + 32s = 30000
14000 + 20000 - 40s + 32s = 30000
34000 - 8s = 30000
-8s = 30000 - 34000
-8s = -4000
s = 
s = +500 acres of soybeans
:
That means that he will plant 0 acres of wheat, to satisfy these requirements
:
:
Check solution:
28(500) + 40(0) + 32(500) =
14000 + 0 + 16000 = 30000
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