170. In a chess tournament, students from the 9th and 10th grades participated. Each participant played against every other participant once. There were 10 times more 10th graders than 9th graders, and they scored 4.5 times more points in total than all the 9th graders. How many 9th grade students participated in the tournament and how many points did they score?
170. Let the number of ninth graders be $n$ and they scored $m$ points. Then the number of tenth graders was $10 n$ and they scored $4.5 m$ points. The total number of participants in the tournament was $11 n$ and they scored 5.5 m points.

The total number of points scored by everyone is equal to the number of games played. The number of games played was $\frac{11 n(11 n-1)}{2}$. Therefore,

$$
5.5 m=\frac{11 n(11 n-1)}{2}
$$

and, consequently,

$$
m=n(11 n-1)
$$

Each ninth grader played $11 n-1$ games (since the number of participants in the tournament is (11n), and therefore $n$ ninth graders could have scored $n(11 n-1)$ points only if each of them won all their games. This is only possible if $n=1$ (since two ninth graders cannot simultaneously win against each other). Thus, we get the only solution $n=1, m=10$.