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  1. #1
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    farmer land

    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 $63750 for the cost of growing his crops. How many acres of each crop should he plant?
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  2. #2
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    Quote Originally Posted by aeroflix View Post
    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 $63750 for the cost of growing his crops. How many acres of each crop should he plant?
    Same basic idea as your "investor"problem. First name your variables: Let c bet the number of acres used to grow corn, w the number of acres used to grow wheat, and s the number of acres used to grow soy bean.

    "A farmer has 1200 acres of land": c+ w+ s= 1200

    "Because of market demand he will grow twice as many acres of wheat as of corn.": w= 2c

    "It costs $45 per acre to grow corn, $60 for wheat, and $50 for soybeans": so c acres of corn, w acres of wheat, and s acres of soybean will cost 45c+ 50w+ 50s dollars.

    Also "He has allocated $63750 for the cost of growing his crops." so we must have
    45c+ 50w+ 50s= 63750.

    Solve the three equations
    c+ w+ s= 1200
    w= 2c
    45c+ 50w+ 50s= 63750

    Since w= 2c, you can replace w by 2c in both other equations. You can then solve the first equation for s and replace s by that in the third equation. Solve that equation for s, then work back for the values of c and w.
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  3. #3
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    guyz,, it should be 2w =c
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    Quote Originally Posted by HallsofIvy View Post
    "Because of market demand he will grow twice as many acres of wheat as of corn.": w= 2c
    I think it's just a simple mistake.

    The 3 equations should be:

    c + w + s = 1200
    c = 2w
    45c + 50w + 50s = 63750

    You replace c with 2w, add like terms and you get:

    3w + s = 1200
    140w + 50s = 63750

    Now solve using simultaneous equation.
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  5. #5
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    it should be 60w
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  6. #6
    Senior Member Educated's Avatar
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    Yes it should...

    I just corrected the c = 2w but I guess there was another mistake...
    In that case it should be:


    c + w + s = 1200
    c = 2w
    45c + 60w + 50s = 63750

    Which means the 2 equations should be:

    3w + s = 1200
    150w + 50s = 63750


    Since that you can spot the mistakes, why don't you show some working of you solving it? You seem to be capable of solving the equation, so can you solve it instead of telling us our mistakes?
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  7. #7
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    i tried w=2c (which is the original eqaution) and it work.. the asnwer matches the answer in the book..

    but im confuse... why its w = 2c when it said the he planted wheat twice as corn
    ???
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  8. #8
    MHF Contributor Unknown008's Avatar
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    If I have twice as apples as pears, then

    a = 2p

    I must double the number of pears so that I have the same number of apples.

    Does it make sense?
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  9. #9
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    twice as apples,, so it should be 2a
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  10. #10
    MHF Contributor Unknown008's Avatar
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    Let's put figures in then.

    I have 10 apples and 5 pears. By how much should I multiply the number of pears if I want them to be 'equal' to the apples?

    10 apples <=> 2(5 pears)
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