let

x = the number of gold medals that Yugoslavia won = the number of bronze medals Brazil won

Yugoslavia won 1 more silver medal than gold medals that is: x + 1 silver medals

Yugoslavia won 1 more bronze medal than silver medals: x + 1 + 1 = x + 2 bronze medals

Brazil win 1 more bronze medal than silver medals or: x - 1 silver medals

Brazil each won 1 more silver medal than gold medals or: x - 1 - 1 = x - 2 gold medals

In all both countries together won 30 medals:

x + x + 1 + x + 2 + x - 2 + x - 1 + x = 30

by solving we find:

x = 5 medals

click here to see the step by step solution of the equation:

Yugoslavia won 5 gold medals.