There are 27 girls and 36 boys who want to participate in a math competition. If each team must have the same ratio of girls and boys what’s the greatest number of teams that can enter?

Since the ratio of girls and boys must be the same in each team, and all the competitors must be involved, it means that each team's ratio of boys : girls must be equal to the total ratio of Boys : Girls = 36 :27= 4 / 3.

Now 4 / 3, the most simplified version of 36 / 27, happens by dividing the numerator & demoninator by 9 (the greatest number it can divide by). So the greatest number will be 9 teams, each of  4 Boys & 3 Girls