I have done every method I know of. The teacher said it took him 2 weeks. I am completely lost.
In a middle school, $79\%$ of the students like basketball, $64\%$ like volleyball, $49\%$ like tennis, $81\%$ like swimming, and $89\%$ like soccer. What is the minimum percentage of students who like $3$ or more sports?
I think this works...
Try stripping away the percents, assume there are 100 students in the school:
What's the smallest number of students who like 3 or more sports?
Summing, we get 89 + 81 + 79 + 64 + 49 = 362, so the average student likes 3.62 sports.
To minimize the total number of students liking 3 or more sports, you will want students that like 3 or more to like as many as possible. And if they like less than 3, they might as well like 2 to eat up as many liked sports as possible.
If the 49 students who like tennis also like the other 4 sports, that's 49 students who like all 5. They're consuming the maximum number of liked sports 5 * 49 = 245 that 49 students could.
That leaves 117 remaining liked sports and 51 remaining students.
We could have 8 students like the four remaining sports, but not tennis. That eats up 4 * 8 = 32 more liked sports.
So at this point we've accounted for 245 + 32 = 277 of the 362 liked sports with 49 + 8 = 57 kids. We have 85 liked sports to go for 43 kids. 42 of them can like 2 sports each and one kid can like just 1 sport.
That gives you a minimum of 57 kids that like at least three sports.
Ultimately, either of these are possible:
Or:
57% like 3 sports either way.