Help with 'A farmer buys 100 animals for $100....'

[Brainiac009]

A farmer buys 100 animals for $100.
Cow=$5
Sheep=$3
Rabbit=$0.50
He baught atleast 1 of each animal.
How many of each animal did he buy?

 

[galactus]

Re: Helllp ASAP!!!!

There are various solutions that will work.

We have 100 animals in all: c+s+r=100...........[1]

They cost $100: 5c+3s+0.5r=100.........[2]

If you solve [1] for c and sub into [2]:

\(\displaystyle c=100-s-r\)

\(\displaystyle 5(100-s-r)+3s+\frac{1}{2}r=100\)

you can solve for r.

Then try whole-number values for s, and see where that takes you.

 

[TchrWill]

A farmer buys 100 animals for $100.
Cow=$5
Sheep=$3
Rabbit=$0.50
He bought at least 1 of each animal.
How many of each animal did he buy?

Alternatively

1--Let C + S + R = 100
2--Let 5C + 3S + .5R = 100 or 10C + 6S + R = 200
3--Subtracting (1) from (2) yields 9C + 5S = 100
4--Dividing through by 5 yields 1C + 4C/5 + S = 20
5--4C/5 must be an integer k...

...so what does that say about C?