Suppose the horse is X, the mare is Y and the pony is Z, then

X+Y+Z= 100 ( 1)

3X+2Y+ 1/2Z= 100 (2)

Y≥20 (3)

(2)*2-( 1)

5X+3Y= 100 (4)

Substitute (3) into (4) to get X≤8.

According to (4), when Y=20, 25 and 30, x has integer solutions of 8, 5 and 2, and Z=72 and 70.68 are obtained by substituting them into (1) respectively.

The three groups of solutions obtained in this way are all effective, and these three groups of solutions are respectively substituted into formula (2) for checking calculation.

So the solution of the equation has {X=8 {X=5 {X=2.

Y=20 Y=25 Y=30

Z=72 Z=70 Z=68

There are 8 big horses, 20 mares and 72 ponies. Or 5 horses, 25 mares, 70 ponies; Or 2 horses, 30 mares and 68 ponies.