[This is inspired by the MLP EQ: Friendship Games movie.]
As much as Fred loved a bit of chaos and mischief as much as the next person (if the next person was George, ofcourse), even he thought the idea of a competition between Hogwarts and a muggle school was a poor idea. However, on top of that, these students would be staying in Hogwarts, meaning the students of Hogwarts could perform magic as normal.
The competition was only supposed to last a month, but a month of having to look over your shoulder all the time to make sure you didn't use magic in front of a muggle was hell. There were several parts of the competition, none of which were 'magical' and most of which were Muggle-based in nature (with some things in the grey area between).
It started with an Academic Decathlon to decide who would be representing each school, with only six people on each team of the students who had gotten the most points from each school. Then, once the teams were decided, there would be the Tri-Cross Relay (which was archery, speed-skating, and motocross) and Capture the Flag.
Somehow, Fred made the team for Hogwarts. Sure, he wasn't stupid by any means, but there were only five other on the Hogwarts teams, including Hermione Granger and Cedric Diggory; it was still a shock.
But then something weird started happening, and Fred suspected it all pointed to the Muggle school's team. His youngest brother, Ron, lost his ability to do magic. Not like in Ron's second year, when he broke his wand and his magic started acting weird. No, he could do anything magic-related. Ofcourse, no one could question the muggle school about it, because then they would have to explain magic to them.
Fred, however, wasn't going to sit by as his youngest brother lost his magic without answers. And in his search for answers, with the assistance of Hermione and Harry, everything pointed to you.
You were a quiet Muggle student who had made the team for the Muggle school, and you seemed nice enough. It was quite confusing how a Muggle of all people had been able to do it, and Fred wouldn't stop until he figured out how you had and if you even knew what you had done.