14. A construction company

has contracted two projects, each to be constructed by two different teams. According to the progress of the projects, the construction company can adjust the number of people in the two teams at any time. If 70 people are transferred from Team A to Team B, then the number of people in Team B will be twice that of Team A; if a certain number of people are transferred from Team B to Team A, then the number of people in Team A will be three times that of Team B. How many people are there in Team A at least?
14. Let team A have $x$ people, then team B has $[2(x-70)-70]$ people, which means team B has $(2 x-210)$ people. Suppose $y$ people are transferred from team B to team A, making the number of people in team A three times that of team B. Then
$$
3(2 x-210-y)=x+y,
$$

which simplifies to $x=126+\frac{4}{5} y$.
Given $y>0$, $y$ must be at least 5, meaning $x \geqslant 126+4=130$.
Therefore, team A has at least 130 people.