# 100 animals 100 dollars? easy? I thought so.

1. Mar 29, 2005

### 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

Last edited: Mar 30, 2005
2. Mar 29, 2005

does the total cost have to be $100 also?? 3. Mar 29, 2005 ### 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, im not sure. i just tried out various values. took me a couple minutes. 4. Mar 29, 2005 ### Data Your system is fine. Solve it to get $$x - \frac{z}{18} = 0, \; y + \frac{19}{18}z = 100$$ so you can choose $z=18 \Longrightarrow x = 1, \; y = 81$. 5. Mar 29, 2005 ### 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.

Last edited: Mar 29, 2005
6. Mar 29, 2005

### JaeSun

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

7. Mar 29, 2005

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. Mar 29, 2005 ### JaeSun its not nickels, but$0.50

9. Mar 29, 2005

### 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.

10. Mar 29, 2005

### JaeSun

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

11. Mar 29, 2005

### JaeSun

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

12. Mar 29, 2005

### Data

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

13. Mar 29, 2005

### Data

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

14. Mar 29, 2005

### tony873004

I get:

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

15. Mar 30, 2005

### Automagman

woops, lol ahaha. I feel retarded. chickens are 50 cents, or 2 quarters. Wow sorry about that.