Ninth- and tenth-grade students participated in a tournament. Each contestant played each other contestant once. There were ten times as many tenth-grade students, but they were able to win only four-and-a-half times as many points as ninth graders.
How many ninth-grade students participated, and how many points did they collect?
Note: one point for every win.
This is another problem not clearly defined. We are not told what games/sports are involved, but only that all compete as pairs (two participants in each game). Since not told otherwise, I shall assume there can be no draws/ties. This is not defined as a contest of one grade vs another, so I shall assume that each contestant played every other contestant of either grade.
The answer is patently obvious: there was one ninth-grader, and ten tenth-graders (ten times as many tenth-graders).
The ninth-grader beat each of the tenth graders, hence scoring 10 points. Clear each tenth-grader lost to that ninth-grader so got no points for those matches. When the tenth-graders played each other, there were 45 games (10*9/2), so the tenth-graders collectively scored 45 points. Their 45 points are 4.5 times the points scored by the ninth-grader (10).
I'll post, and then look at other comments. What is supposed to be the point of the problem?
Obvious solution
