Let's assume the number of gold medals won by Finland is x.
According to the first statement, Germany won three times as many gold medals as Finland, so the number of gold medals won by Germany is 3x.
According to the second statement, if Germany had won three more than three times their number of gold medals, it would have won twelve more gold medals than Estonia. So, we can form the equation:
3x + 3 = 12 + (1/3) * (3x + 3)
Simplifying this equation:
3x + 3 = 12 + x + 1
2x = 10
x = 5
Therefore, Finland won 5 gold medals.
According to the third statement, Finland won one fewer gold medal than one-third of the number of gold medals won by Estonia. So, we can form another equation:
5 = (1/3) * (3x + 3 - 1)
5 = (1/3) * (3x + 2)
Multiplying both sides by 3:
15 = 3x + 2
3x = 15 - 2
3x = 13
x = 13/3
Therefore, Estonia won 13 gold medals.
Since Germany won three times as many gold medals as Finland, Germany won 3 * 5 = 15 gold medals.
To summarize:
- Finland won 5 gold medals.
- Germany won 15 gold medals.
- Estonia won 13 gold medals.