The Farmers Puzzle?

Question

$100 dollars a farmer paid for 100 animals - Sheep were $10
Pig were $2 and Hens were .50c , What did she do

Answer 1

as above:
10s+2p+0.5h=100
s+p+h=100
there is no third equation, but there is a condition that s,p,h are positive integers.
from the 2 equations
9.5s+1.5p=50 ==> 19s+3p=100 ==> s=(100-3p)/19 and p=(100-19s)/3
for s to be integer (100-3p) must be divisable by 19 and >0
i.e
100-3p= 0,19,38,57,76 or 95 i.e. s=0, 1, 2, 3, 4 or 5
p will be integer when s=1 and 4
at s=1 p=27
at s=4 p=8
from the first equation:
at s=1: 10*1+2*27+h*0.5=100 ==> h=72
at s=4: 10*4+2*8+h*0.5=100 ==> h=88
so we have two solutions:
one sheep, 27 pigs and 72 hens
or 4 sheeps, 8 pigs and 88 hens

Answer 2

what else,the farmer bought 100 animals with that money.

Answer 3

bought 100 chickens for $1 each :)

Answer 4

10s+2p+0.5h=100
s+p+h=100

we need one more equality!