SOLUTION: A farmer has 1200 acres of land on which he grows corn, wheat and soybeans. It costs $45 per acre to grow corn, $60 for wheat, and $50 for soybeans. Because of market demand he w

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: A farmer has 1200 acres of land on which he grows corn, wheat and soybeans. It costs $45 per acre to grow corn, $60 for wheat, and $50 for soybeans. Because of market demand he w      Log On


   



Question 323383: A farmer has 1200 acres of land on which he grows corn, wheat and soybeans. It costs $45 per acre to grow corn, $60 for wheat, and $50 for soybeans. Because of market demand he will grow twice as many acres of wheat as of corn. He has allocated $63,750 for the cost of growing his crops. How many acres of each crop should he plant?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.C%2BW%2BS=1200
2.45C%2B60W%2B50S=63750
3.W=2C
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.
.
Substitute eq. 3 into eq. 1 and eq. 2,
C%2B2C%2BS=1200
4.3C%2BS=1200
.
.
.
45C%2B120C%2B50S=63750
5.165C%2B50S=63750
Multiply eq. 4 by (-50) and add to eq. 5 to eliminate S,
-150C-50S%2B165C%2B50S=-60000%2B63750
15C=3750
highlight%28C=250%29
highlight%28W=500%29
Then use eq. 4 to solve for S,
750%2BS=1200
highlight%28S=450%29