100 animals 100 dollars? easy? I thought so.

[Automagman]

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

 

[JaeSun]

does the total cost have to be $100 also??

 

[JaeSun]

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, I am not sure.

i just tried out various values. took me a couple minutes.

 

[Data]

Your system is fine. Solve it to get

$$x - \frac{z}{18} = 0, \; y + \frac{19}{18}z = 100$$

so you can choose $z=18 \Longrightarrow x = 1, \; y = 81$.

 

[robert Ihnot]

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.

 

[JaeSun]

nope ... the number of chickens is not a multiple of 20

 

[robert Ihnot]

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?

 

[JaeSun]

its not nickels, but $0.50

 

[Data]

oops, i used $0.5 for $z$~

There's no positive integer $z$ that also makes $x$ and $y$ positive integers that satisfies the system if it's really $0.005.

 

[JaeSun]

at least for my answer and what he wrote above (.5) which i took as 50 cents

 

[JaeSun]

i had a different answer

4 cows = $40
24 pigs = $24
72 chickens = $36
===============
100 animals at $100

 

[Data]

It's even worse than nickels. The way that he stated it it was half-pennies.

 

[Data]

Yes, there are several possible answers if a chicken costs $0.5.

 

[tony873004]

I get:

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

 

[Automagman]

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