2025 AMC 10A Problem 4

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 \qquad \textbf{(B)} 29 \qquad \textbf{(C)} 30 \qquad \textbf{(D)} 32 \qquad \textbf{(E)} 33

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.