8 chickens and 12 ducks.

Let c represent the number of chickens. Let d represent the number of ducks.

The total number of animals bought was 20. So c + d = 20.

The man received a $2 discount per chicken and a $0.50 discount per duck. The total discount he received was $22. So 2c + 0.50d = 22.

Now we have two equations with two varaibles. First we will rewrite the first equation to find the value of c.
c + d = 20
c = 20 - d

Now we can substitue the vale of c from above into the second equation and solve for d.
2c + 0.50d = 22
2(20 - d) + 0.50d = 22
40 - 2d + 0.50d = 22
40 - 1.50d = 22
-1.50d = -18
d = 12

Now solve for c in the first equation.
c + d = 20
c + 12 = 20
c = 8

 

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