2025 AMC 8 Problems/Problem 10

There are fifty $1, $2, and $5 notes. There are two more $1 notes than $2 notes. Given that the total value of the notes is $116, find the number of $5 notes.

$\textbf{(A) } 9\qquad\textbf{(B) } 10\qquad\textbf{(C) } 11\qquad\textbf{(D) } 12\qquad\textbf{(E) } 13$