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100 animals 100 dollars? easy? I thought so.

  1. Mar 29, 2005 #1
    I have to buy 100 animals, I have to use 100 dollars, I have to get at least 1 of each.

    Cow(X) = 10 bucks
    Pig(Y) = 1 buck
    Chicken(Z) = .5 bucks, 50 cents, 2 quarters

    This looked really easy at first but I kept getting stuck, how do I get through this?

    Restraints I came up with.

    x+y+z=100
    10x+1y+.5z=100
    X is greater than or equal to 1 and is less than or equal to 10
    Y is greater than or equal to 1
    Z is greater than or equal to 1
     
    Last edited: Mar 30, 2005
  2. jcsd
  3. Mar 29, 2005 #2
    does the total cost have to be $100 also??
     
  4. Mar 29, 2005 #3
    i have the answer!

    hint:

    x (cows) can be reasonably guessed.

    then you go from there

    (this is how i did it. trial and error.lol)

    only problem is, if you have to show work in terms of math, im not sure.

    i just tried out various values. took me a couple minutes.
     
  5. Mar 29, 2005 #4
    Your system is fine. Solve it to get

    [tex]x - \frac{z}{18} = 0, \; y + \frac{19}{18}z = 100[/tex]

    so you can choose [itex]z=18 \Longrightarrow x = 1, \; y = 81[/itex].
     
  6. Mar 29, 2005 #5
    Data: so you can choose z=18,x=1,y=81
    But, that fails to equal $100, since we have 10x1+1x81+.05x18 =$91.90.

    Frankly, the number of chicken must be a multiple of 20, since the other monetary values are in dollars. Then while we are at it, the cost of the pigs and the chickens must be a multiple of $10.
     
    Last edited: Mar 29, 2005
  7. Mar 29, 2005 #6
    nope ... the number of chickens is not a multiple of 20
     
  8. Mar 29, 2005 #7
    If the total cost is to be $100 how are we to get rid of the odd nickels if the chickens are not a multiple of 20? Are you planning to add a tax?
     
  9. Mar 29, 2005 #8
    its not nickels, but $0.50
     
  10. Mar 29, 2005 #9
    oops, i used $0.5 for [itex]z[/itex]~

    There's no positive integer [itex]z[/itex] that also makes [itex]x[/itex] and [itex]y[/itex] positive integers that satisfies the system if it's really $0.005.
     
  11. Mar 29, 2005 #10
    at least for my answer and what he wrote above (.5) which i took as 50 cents
     
  12. Mar 29, 2005 #11
    i had a different answer

    4 cows = $40
    24 pigs = $24
    72 chickens = $36
    ===============
    100 animals at $100
     
  13. Mar 29, 2005 #12
    It's even worse than nickels. The way that he stated it it was half-pennies.
     
  14. Mar 29, 2005 #13
    Yes, there are several possible answers if a chicken costs $0.5.
     
  15. Mar 29, 2005 #14

    tony873004

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    Science Advisor
    Gold Member

    I get:

    x,y,z
    1, 81, 18
    2, 62, 36
    3, 43, 54
    4, 24, 72
    5, 5, 90
     
  16. Mar 30, 2005 #15
    woops, lol ahaha. I feel retarded. chickens are 50 cents, or 2 quarters. Wow sorry about that.

    note- made a few changes to my first post to answer some of your questions
     
    Last edited: Mar 30, 2005
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