6th Grade Fractions and Proportions: Problem 3

Problem: The original number of male athletes to female athletes at an event was 19:12. This year, the judges decided to add some more female events, causing the number male athletes to female athletes to become 20:13. And then, they had some more ideas for male events and added that, too. The ratio of male athletes to female athletes became 30:19. The number of male athletes who joined after the new events was 15 athletes more than the number of female athletes who joined after the new events. Now, what is the total amount of athletes?

Key: Find equivalent ratios of given ones so that the units make sense

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