Answer
Australia = 6
Germany = 7
Korea = 8
Work Step by Step
Let a = no. of gold medals won by Australia
Let g = no. of gold medals won by Germany
Let k = no. of gold medals won by Korea
Since the numbers are consecutive:
g = a + 1
k = (a + 1) + 1 = a + 2
Since the total number of medals is 21:
a + g + k = 21
a + (a+1) + (a+2) = 21
3a + 3 = 21
3a = 18
a = 6
a=6, g = 7, k = 8