14. (15 points) The teacher gives fruits to students, preparing two types of fruits. The number of oranges is 3 more than 3 times the number of apples. If each student gets 2 apples, there will be 6 apples left; if each student gets 7 oranges, the last student can only get 1 orange. Find the number of students.


【Analysis】This problem can be solved using the method of equations. Expressing the quantitative relationships in the problem will allow us to set up the equations.
【Solution】Solution: According to the problem, we have:
Let the number of students be $x$ people. Then the number of apples is $2 x+6$ and the number of oranges is $7(x-1)+1$. Therefore, we can get:
$$
\begin{array}{r}
(2 x+6) \times 3+3=7(x-1)+1 \\
6 x+21=7 x-6 \\
x=27
\end{array}
$$

Answer: There are 27 students.