AMC 12 2025a Problem 3

A team of students is going to compete against a team of teachers in a trivia contest. The total number of students and teachers is $15$. Ash, a cousin of one of the students, wants to join the contest. If Ash plays with the students, the average age on that team will increase from $12$ to $14$. If Ash plays with the teachers, the average age on that team will decrease from $55$ to $52$. How old is Ash?

\textbf{(A)}~28 \textbf{(B)}~29 \textbf{(C)}~30 \textbf{(D)}~32 \textbf{(E)}~33