Question

100 animals for $100
1 pig=$2.50
1 chicken=$0.50
1 cow=$10

Answer 1

well, one way is
40 pigs

I'm sure you can find others.

Answer 2

pigs --- x
chicks --- y
cows --- 100-x-y

2.5x +.50y + 10(100 - x-y) = 100
2.5x + .5y + 1000 - 10x - 10y = 100
-7.5x - 9.5y = -900
75x + 95y = 9000
15x + 19y = 1800

19y = 1800-15x = 15(120 - x)
120-x must be a multiple of 19 , 0 ≤ x ≤ 6
a quick check for x shows if
x = 6
y = 15(114)/19 = 90
z = 100-6-90 = 4

So there 6 pigs ---- cost = $15
90 chickens --- cost = $45
4 cows ---- cost = $40

total cost = 15+45+40 = 100
number of animals = 6+90+4 = 100

I have the right answer