Question 8459
 Your equations and idea are correct.
 However, tn fact,there is no third equation to help you to solve this system.

 This kind of system,we can call it linear integer equations:
 [It may have nfinite many integer solutions or no integer solutions]
 X + Y + Z = 1000..(1)
.2X + .5Y + 2Z = 1000...(2)

 (2)*10 to get rid of decimals:
 2X + 5Y + 20 Z = 10000...(3)

 (3)-(1)*2: 3y + 18 z = 8000
 We see that the left hand side is divisible by 3, but the right 
 hand side is not. Hence, this system has no integer solutions.

 In other words,there are no coins X,Y,Z can make the two 1000s.
 And, hence, nobody can get the reward el mundo. 

 Kenny