2024 AMC 12B Problem 10

A list of 9 real numbers consists of 1, 2.2, 3.2, 5.2, 6.2, and 7, as well as x, y,z with x\leq y\leq z. The range of the list is 7, and the mean and median are both positive integers. How many ordered triples (x,y,z) are possible?

\textbf{(A) }1 \qquad\textbf{(B) }2 \qquad\textbf{(C) }3 \qquad\textbf{(D) }4 \qquad\textbf{(E) }\text{infinitely many}\qquad

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