22) In a scientific high school there are fewer than 1000 students, of which 230 attend the triennial classes; the students who attend the second year are $\frac{13}{46}$ of all the remaining; furthermore, if 10 more students were to enroll in the first year, then the first-year students would become $\frac{2}{5}$ of the total. The number of students in the school is:
(A) 500
(B) 590
(C) 625
(D) 700
(E) 825.
22) The answer is (B). Let $n_{1}, n_{2}, n_{3}$ be the number of students attending the first, second, and third year, respectively. The following relationships are given: $\left\{\begin{array}{l}n_{2}=\frac{13}{46}\left(n_{1}+n_{3}\right) \\ n_{1}+10=\frac{2}{5}\left(n_{1}+n_{2}+n_{3}+10\right) \\ n_{3}=230\end{array}\right.$ from which $\left\{\begin{array}{l}-13 n_{1}+46 n_{2}=2990 \\ 3 n_{1}-2 n_{2}=430\end{array}\right.$ and finally $n_{1}=230, n_{2}=130$ and the total number of students is therefore 590.