SOLUTION: The Willey Farm Collective, farmed by several branches of the Willeys, has 4500 acres of land available for raising corn and soybeans. The cost of raising corn is $42 an acre, whil

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The Willey Farm Collective, farmed by several branches of the Willeys, has 4500 acres of land available for raising corn and soybeans. The cost of raising corn is $42 an acre, whil      Log On


   

Question 577875: The Willey Farm Collective, farmed by several branches of the Willeys, has 4500 acres of land available for raising corn and soybeans. The cost of raising corn is $42 an acre, while the cost of wheat is $35 an acre. The Collective's available capital is $165,200. How many acres of each species should the Collective plant?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = acres planted in corn
Let b = acres planted in wheat
given:
(1) +a+%2B+b+=+4500+
(2) +42a+%2B+35b+=+165200+
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The solution has to be on the line
(1) in an area where (2) is true
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(1) +b+=+4500+-+a+
Substitute (1) into (2)
(2) +42a+%2B+35%2A%28+4500+-+a+%29+=+165200+
(2) +42a+%2B+157500+-+35a+=+165200+
(2) +7a+%3C=+165200+-+157500+
(2) +7a+=+7700+
(2) +a+=+1100+
And, from (1)
(2) +4500+-+b+=+1100+
(2) +-b+=+-+3400+
(2) +b+=+3400+
1100 acres should be planted in corn
3400 acres should be planted in wheat
here's the plots: