c=number of cows, h=number of hogs, k=number of chickens
c+h+k=100
10c +5h +.5k =100 0r 20c +10h +k =200
subtracting the first equation from the second gives
19c +9h =100
19c =100 -9h
when h=1, 100-9h =91
when h=2, 100-9h =82
when h=3, 100-9h =73
(we are looking for a multiple of 19:19,38, 57, 76, ...)
when h=4, 100-9h =64
when h=5, 100-9h =55
when h=6, 100-9h=46, ...
when h=9, 100-9h =19 and c=1
If there is one cow and 9 hogs then there are 90 chickens
1 x$10 + 9 x $5 +90 x$0.50 =$100