Question 707095
w cow ____________$5 each
p pig ____________$1 each 
n chicken ________$0.50 each


w+p+n=100, farmer bought 100 animals
Examining the cost: 5*w+1*p+0.5*n=100, farmer spent 100 dollars


w>=1, p>=1, n>=1


By chance, I assumed w=k, just some assumed natural number, and solved the system for p and n.  I only used simple algebra-1 stuff; no matrix operations.  

Work was then done on system:
p+0.5n=100-5k
p+n=100-k


My initial results were w=k, p=100-9k, n=8k.  
One of the specifications was that at least one animal of each kind was bought.  I tried k=1 and computed what that would do for w, p, and n.  Good results:  if k=1, then w=1, p=91, and n=8.  Total 100 animals.