future

hello teacher

Ari: By the time we get to the movie theater, the tickets are going to be sold out.
Sarah: Don't worry. I told Jane we might be arriving just before the movie starts . She is going to buy our tickets and meet us in the lobby.
Ari: That place is huge! We will never find her in that crowded lobby.
Sarah: Calm down, we are going to meet each other near the entrance.

Would have been possible to write*she is buying* and *we are meeting * because if she is buying and if we are meeting at the entrance , both action should have been decided before like an arrangement o for an arrangement present progressive is better.

Please could you let me know what you think ?