Heidi invited us to have a dinner, why?

第一个句子: I'll treat!==My treat! 我请客!

I want to invite you to dinner. I'll treat!

第二个句子: It's a deal! 一言为定!

第三个句子: Let's go fifty-fifty. AA制!

Reference:

a. Are you free tomorrow? I want to treat you to dinner.

b. Is it a deal?

a. It's a deal.

b. So see you at the old school gate.

a. See you and be there or be square!

b. See you!