Question

I need to buy 100 farm animals with $100.. I need to have brought at least on of each animal. Roosters are $5ea, Hens $3ea and chickens 3 for $1.

Can anyone help???

Answer 1

We solve the system
R+H+C=100
5R+3H+(1/3)C=100, where R,H,C are natural.

R=100-H-C
15R+9H+C=300

15(100-H-C)+9H+C=300
6H+14C=1200
3H+7C=600, H+C<100
H=18, C=78--> R=4
H=11, C=81--> R=8
H= 4, C=84--> R=12

Answer 2

Try any combination that spends $100:
30 chickens for $10
10 hens for $30
12 roosters for $60
gives a total of 52 animals for $100.

We need 100-52=48 more animals.

By exchanging a rooster for chickens, we get 14 more animals for the same price. Similarly, by exchanging a hen for chickens, we get 8 more animals for the same price.

We have to solve the equation
14R + 8H = 48
where
R=number of roosters to exchange, and
H=number of hens to exchange

We can solve it using R=0, and H=6.

we would finally get
30+18*3=84 chickens for $28
10-6=4 hens for $12
12 roosters for $60
Total 100 animals for $100.

There may be other solutions.

Answer 3

yep thanks guys... got it before anyone responded but once again thanks