100 animals 100 dollars? easy? I thought so.

  • Thread starter Automagman
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  • #1
15
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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:

Answers and Replies

  • #2
37
0
does the total cost have to be $100 also??
 
  • #3
37
0
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.
 
  • #4
998
0
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].
 
  • #5
1,056
0
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.
 
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  • #6
37
0
nope ... the number of chickens is not a multiple of 20
 
  • #7
1,056
0
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?
 
  • #8
37
0
its not nickels, but $0.50
 
  • #9
998
0
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.
 
  • #10
37
0
at least for my answer and what he wrote above (.5) which i took as 50 cents
 
  • #11
37
0
i had a different answer

4 cows = $40
24 pigs = $24
72 chickens = $36
===============
100 animals at $100
 
  • #12
998
0
It's even worse than nickels. The way that he stated it it was half-pennies.
 
  • #13
998
0
Yes, there are several possible answers if a chicken costs $0.5.
 
  • #14
tony873004
Science Advisor
Gold Member
1,751
143
I get:

x,y,z
1, 81, 18
2, 62, 36
3, 43, 54
4, 24, 72
5, 5, 90
 
  • #15
15
0
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
 
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