Question 152198
Let x be the prize for the third place, then the prize for the second place is x + 4 and the prize for the second place is x + 4 + 5 = x + 9.
As the total prize money is $52, we can set up an equation:
(x) + (x + 4) + (x + 9) = 52
Solving the equation for x, we have
3x + 13 = 52
3x = 39
x = 13
So 
The prize for the third place is 13.
The prize for the second place is 17.
The prize for the first place is 22.