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Thread: How To solve

20080722, 18:09 #1
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How To solve
I was sent this puzzle, I solved it by deduction and trial and error. It is keeping me awake at night trying to solve it with maths, any help appreciated.
Farmer Tony Smith bought 100 animals for his new farm.
He paid $300 each for the chickens, $800 each for the guinea pigs and $2100 each for the geese.
Tony spent a total of $60000
Tony could not remember how many of each animal he had bought.
However, he did remember that there was an even number of geese!
Can you work out how many of each animal Tony bought?

20080722, 22:01 #2
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Re: How To solve
Is there anything you cannot achieve. Yes the answer is the same as I got. I again thank you

20080722, 22:26 #3
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Re: How To solve
<span style="backgroundcolor: #FFFF00; color: #FFFF00; fontweight: bold">Let's designate the number of chickens, guinea pigs and geese by x, y and z, respectively.
x + y + z = 100 (1)
3x + 8y + 21z = 600 (2)
Subtract equation (1) three times from equation (2)
5y + 18z = 300
Since 5y and 300 are divisible by 5, z must be divisible by 5. And z is even, so z must be divisible by 10.
Solution 1: z = 0, so 5y = 300 from which follows y = 60 and since the total is 100, x = 40.
40 chickens = $120, 60 guinea pigs = $480, 0 geese = $0, total $600.
If you assume that he bought at least one of each, this solution is rejected.
Solution 2: z = 10, so 5y + 180 = 300 from which follows y = 24 and since the total is 100, x = 66.
66 chickens = $198, 24 guinea pigs = $192, 10 geese = $210, total $600.
The next value for z would be 20, but 18*20 is more than 300 so that isn't possible.</span hide>

20080722, 23:27 #4
Re: How To solve
I don't think Hans has quite achieved walking on water <img src=/S/grin.gif border=0 alt=grin width=15 height=15>

20080722, 23:47 #5
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Re: How To solve
In my opinion there has not been a need, just you wait and see.
I was slow in my initial response, I haven't asked him yet.

20080723, 04:06 #6
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Re: How To solve
Why bother when you can simply make it part in your path? <img src=/S/grin.gif border=0 alt=grin width=15 height=15>
Alan

20080723, 04:50 #7
Re: How To solve
Isn't that Claude's trick when discovered in his cellar? He simply points towards the stack of empty Penfold's Bin 707 bottles and says, "Look, I'm just making my way through the red, see?".
<img src=/S/grin.gif border=0 alt=grin width=15 height=15>

20080723, 15:06 #8
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Re: How To solve
<img src=/S/pun.gif border=0 alt=pun width=22 height=18>... where's <img src=/S/queen.gif border=0 alt=queen width=19 height=20> when you need her?
Alan